IEEE Transactions on Information Theory

Volume 29 Issue 3 • May 1983

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Displaying Results 1 - 25 of 31
  • On the inequivalence of generalized Preparata codes

    Publication Year: 1983, Page(s):345 - 348
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (620 KB)

    Ifmis odd andsigma /in Aut GF(2^{m})is such thatx rightarrow x^{sigma^{2}-1}is1-1, there is a[2^{m+1}-1,2^{m+l}-2m-2]nonlinear binary codeP(sigma)having minimum distance 5. All the codesP(sigma)have the same distance and weight enumerators as the usual Preparata codes (which rise asP(sigma)whenx^{sigma}=x^... View full abstract»

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  • Perfect codes hardly exist

    Publication Year: 1983, Page(s):349 - 351
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (411 KB)

    The main lines of a partial proof of the "perfect code theorem" are presented. The relevant part refers to the nonexistence of unknownt-perfect codes over arbitrary alphabets fort not in {1, 2, 6, 8}. The details of the proof can be found in the author's Ph.D. dissertation at the University of Amsterdam. View full abstract»

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  • A nonconstructive upper bound on covering radius

    Publication Year: 1983, Page(s):352 - 353
    Cited by:  Papers (34)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (187 KB)

    Lett(n,k)denote the minimum covering radius of a binary linear(n,k)code. We give a nonconstructive upper bound ont(n,k), which coincides asymptotically with the known lower bound, namelyn^{-1}t(n,nR)=H^{-1}(1-R)+O(n^{-l}log n), whereRis fixed,0<R<1, andH^{-1}is the inverse of the binary entropy function. View full abstract»

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  • The covering radius of the(2^{15}, 16)Reed-Muller code is at least 16276

    Publication Year: 1983, Page(s):354 - 356
    Cited by:  Papers (61)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (349 KB)

    Two interesting cosets of the first-order Reed-Muller code of block length2^{15}are described. They provide counterexamples to a conjecture on the covering radius. View full abstract»

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  • Another upper bound on covering radius

    Publication Year: 1983, Page(s):356 - 359
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (614 KB)

    A new upper bound on the covering radius of binary linear codes improves on previously known bounds for some codes. The bound is[W/2]+rho_{2}, whereWis one of the weights occurring among the codewords, andrho_{2}is the covering radius of an associated code. Some comparisons with other bounds are made. View full abstract»

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  • On the coveting radius of extremal self-dual codes

    Publication Year: 1983, Page(s):359 - 363
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (552 KB)

    It is known that every self-dual binary code which is not doubly even is a "child" of a doubly even parent. It will be shown that an(n-2,(n-2)/2)child of an(n,n/2,d)doubly even parent has covering radiusgeq d-1. Every extremal doubly even(32,16,8)code has covering radius6and every extremal doubly even(48,24,12)code has covering radi... View full abstract»

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  • Cyclic self-dual codes

    Publication Year: 1983, Page(s):364 - 366
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (350 KB)

    It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to2modulo4. In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial code in this class is shown... View full abstract»

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  • The binary code arising from a 2-design with a nice collection of ovals

    Publication Year: 1983, Page(s):367 - 369
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (428 KB)

    A theorem for a binary code arising from a2-design is presented. View full abstract»

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  • On the uniqueness of a certain thin near octagon (or partial 2-geometry, or parallelism) derived from the binary Golay code

    Publication Year: 1983, Page(s):370 - 371
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (231 KB)

    The question of the uniqueness of a certain combinatorial structure has arisen in three contexts: a) is the regular near octagon with parameters(s,t_{2},t_{3},t)=(1, 1,2,23)unique [5]? b) is the partial2-geometry with nexus three and blocksize24unique [2]? c) is there a unique graph such that it is the graph of a parallelism ofleft(^{24}_{4}right)with re... View full abstract»

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  • The construction of fast, high-rate, soft decision block decoders

    Publication Year: 1983, Page(s):372 - 377
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (792 KB)

    A detailed description is given of a fast soft decision decoding procedure for high-rate block codes. The high speed is made possible (in part) by using the symmetries of the code to simplify the syndrome decoding by table look-up and by making the best use of the soft decision information. The(128,106,8)BCH code is used as an example. View full abstract»

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  • Improving an algorithm for factoring polynomials over a finite field and constructing large irreducible polynomials

    Publication Year: 1983, Page(s):378 - 385
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1203 KB)

    Letf(x)in {bf F}_{q}[X]be a polynomial with simple roots to be factored. The so-called Berlekamp subalgebraBspanned over{bf F}_{q}by the idempotents ofA={bf F}_{q}[X]/(f(X))is considered. An exponential technique introduced earlier is based upon taking elements from B at random and enables us to obtain idempotents and, from that, the factors of f(X). Thi... View full abstract»

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  • Upper bounds on|C_2|for a uniquely decodable code pair(C_1, C_2)for a two-access binary adder channel

    Publication Year: 1983, Page(s):386 - 389
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (448 KB)

    An algebraic and a combinatorial upper bound are derived on|C_{2}|given the codeC_{1}, where(C_{l}, C_{2})is a uniquely decodable code pair(C_{1}, C_{2})for a two-access binary adder channel. A uniquely decodable code with rate pair(0.5170, 0.7814)is also described. View full abstract»

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  • Successive encoding of correlated sources

    Publication Year: 1983, Page(s):390 - 395
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (826 KB)

    The encoding of a discrete memoryless multiple source{( X_{i}, Y_{i})}_{i=1}^{infty}for reconstruction of a sequence{Z_{i}}_{i=1}^{infty}}, withZ_{i} = F( X_{i}, Y_{i}); i = 1,2, cdotsis considered. We require that the encoding should be such that{X_{i}}_{i=1}^{infty}is encoded first without any consideration of{Y_{i}}_{i=1}^{infty}, while in ... View full abstract»

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  • New constructions of codes meeting the Griesmer bound

    Publication Year: 1983, Page(s):434 - 439
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (807 KB)

    For any binary linear( n , k , d)code the Grfesmer bound says thatn geq sum_{i=0}^{k-1} lceil d/2^{i} rceil. We investigate codes that meet this bound with equality. We give new descriptions of(sum_{i=0}^{k-1}lceil d/2^{i} rceil , k, d)codes that have earlier been constructed by Solomon and Stiffler, Belov, and Helleseth and van Tilborg. Finally we show how to cons... View full abstract»

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  • Writing on dirty paper (Corresp.)

    Publication Year: 1983, Page(s):439 - 441
    Cited by:  Papers (2220)  |  Patents (112)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (486 KB)

    A channel with outputY = X + S + Zis examined, The stateS sim N(0, QI)and the noiseZ sim N(0, NI)are multivariate Gaussian random variables (Iis the identity matrix.). The inputX in R^{n}satisfies the power constraint(l/n) sum_{i=1}^{n}X_{i}^{2} leq P. IfSis unknown to both transmitter and receiver then the capacity is View full abstract»

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  • On an extension of an achievable rate region for the binary multiplying channel (Corresp.)

    Publication Year: 1983, Page(s):445 - 448
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (689 KB)

    Shannon showed that for the binary multiplying channel (BMC) his inner and outer hounds to the capacity region differ. Schalkwijk gave a simple coding strategy that yields rate pairs(R_{1}, R_{2})outside the Shannon inner bound region. For the case of equal rates in both directions this strategy achievesR_{1} = R_{2} = 0.6 1914beyond Shannon's inner bound rateR_{1} = R_{... View full abstract»

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  • Maximum likelihood decoding of certain Reed - Muller codes (Corresp.)

    Publication Year: 1983, Page(s):448 - 450
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (527 KB)

    We present an efficient maximum likelihood decoding algorithm for the punctured binary Reed-Muller code of order(m - 3)and length2^{m} - 1, M geq 3, and we give formulas for the weight distribution of coset leaders of such codes. View full abstract»

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  • Suboptimum detection of weak signals in non-Gaussian noise (Corresp.)

    Publication Year: 1983, Page(s):462 - 466
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (752 KB)

    A suboptimum detector structure is developed for the detection of weak signals in non-Gaussian noise. In contrast to locally optimum detectors, the suboptimum detector structure is relatively easy to implement and is shown to perform well for a wide range of underlying noise distributions. The robustness of simple limiter detectors is discussed. The extension of the concept of a suboptimum detecto... View full abstract»

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  • Moving window detection for discrete data (Corresp.)

    Publication Year: 1983, Page(s):457 - 462
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (792 KB)

    The moving window detection procedure for discrete data is studied. Bounds for the probabilities and expected values of the waiting time for a detection are derived. The bounds are evaluated for independent identically distributed zero-one Bernoulli trials, binomial, and Poisson random variables, and also for the two-state stationary Markov chain. The results are applicable to the theory of radar ... View full abstract»

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  • A note on first passage time problems for Gaussian processes and varying boundaries (Corresp.)

    Publication Year: 1983, Page(s):454 - 457
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (552 KB)

    First and second-order approximations to the first passage time conditional probability density function of a stationary Gaussian process, with differentiable sample paths crossing a time-dependent boundary, are explicitly provided. In the limit of infinitely large time, our results coincide with the well-known results of Kac and Rice for the constant level-crossing problem. View full abstract»

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  • The discrete memoryless multiple access channel with partially cooperating encoders (Corresp.)

    Publication Year: 1983, Page(s):441 - 445
    Cited by:  Papers (163)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (768 KB)

    We introduce the communication situation in which the encoders of a multiple access channel are partially cooperating. These encoders are connected by communication links with finite capacities, which permit both encoders to communicate with each other. First we give a general definition of such a communication process (conference). Then, by proving a converse and giving an achievability proof, we... View full abstract»

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  • Divisors of codeword weights

    Publication Year: 1983, Page(s):337 - 342
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    The exponent of a nonzero linear code over a finite field of characteristic p is the exponent in the highest power of p dividing the weights of all the codewords. If the code is a right ideal in a group algebra the exponent is related to invariant multilinear forms on the code. This expository paper presents recent results obtained from that relation, extending earlier work of Delsarte and McEliec... View full abstract»

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  • On the stability of signal detection

    Publication Year: 1983, Page(s):426 - 433
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1440 KB)

    The probabilities of false alarm and false dismissal for sure signals embedded in additive noise when the noise is contaminated Gaussian are studied. View full abstract»

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  • A square root bound on the minimum weight in quasi-cyclic codes

    Publication Year: 1983, Page(s):332 - 337
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (576 KB)

    We establish a square root bound on the minimum weight in the quasi-cyclic binary codes constructed by Bhargava, Tavares, and Shiva. The proof rests on viewing the codes as ideals in a group algebra over GF (4). Theorem 6 answers a question raised by F. J. MacWilliams and N. J. A. Sloane in {em The Theory of Error-Correcting Codes.} Theorems 3, 4, and 5 provide information about the way the nonzer... View full abstract»

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  • Estimation of spatial and spectral parameters of multiple sources

    Publication Year: 1983, Page(s):412 - 425
    Cited by:  Papers (34)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2024 KB)

    The problem of estimating spatial and spectral parameters of multiple sources by sensor arrays is considered. A parametric model is derived for the multichannel measurement vector. Tbe model parameters are the time delays and the autoregressive moving-average parameters of all the sources. A suboptimal parameter estimation procedure is proposed, and simulation results are presented to illustrate i... View full abstract»

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IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

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Editor-in-Chief
Prakash Narayan 

Department of Electrical and Computer Engineering