# IEEE Transactions on Information Theory

## Filter Results

Displaying Results 1 - 25 of 45
• ### All Reed-Muller codes are linearly representable over the ring of dual numbers over Z2

Publication Year: 1999, Page(s):700 - 701
Cited by:  Papers (4)
| |PDF (120 KB)

The statement given in the title is proved. Linear codes over chain rings (commutative and noncommutative) are a natural generalization of linear codes over finite fields and of linear codes over integer residue class rings of prime power order. In matters of linear representability there is no obvious reason why we should prefer one chain ring to the other. Yet, apart from Z4, there is... View full abstract»

• ### Every binary (2m-2, 22(m)-2-m, 3) code can be lengthened to form a perfect code of length 2m-1

Publication Year: 1999, Page(s):698 - 700
Cited by:  Papers (6)
| |PDF (168 KB)

We answer a problem posed by Etzion and Vardy (1998) by showing that a binary code of length N=2(m)-2 with 2(N-m) codewords and minimum distance three can always be lengthened to form a perfect code of length 2(m-1) View full abstract»

• ### Asymptotic optimality of likelihood ratio threshold tests in decentralized detection

Publication Year: 1999, Page(s):572 - 585
Cited by:  Papers (5)
| |PDF (748 KB)

Two distributed systems are considered for discriminating between two finite-alphabet bivariate memoryless sources and for detecting a known signal in stationary bivariate additive Gaussian noise. Each system comprises two sensors, M-ary local quantizers and a fusion center which makes decisions based on quantized source observations. The problem of asymptotically optimal quantization is considere... View full abstract»

• ### Linear complexity of de Bruijn sequences-old and new results

Publication Year: 1999, Page(s):693 - 698
Cited by:  Papers (11)
| |PDF (308 KB)

The linear complexity of a de Bruijn sequence is the degree of the shortest linear recursion which generates the sequence. It is well known that the complexity of a binary de Bruijn sequence of length 2n is bounded below by 2n-1+n and above by 2n-1 for n⩾3. We briefly survey the known knowledge in this area. Some new results are also presented, in particular, ... View full abstract»

• ### The second and third generalized Hamming weights of Hermitian codes

Publication Year: 1999, Page(s):709 - 712
Cited by:  Papers (12)
| |PDF (168 KB)

We determine the second and third generalized Hamming weights of all Hermitian codes View full abstract»

• ### An information criterion for likelihood selection

Publication Year: 1999, Page(s):562 - 571
Cited by:  Papers (8)
| |PDF (484 KB)

For a given source distribution, we establish properties of the conditional density achieving the rate distortion function lower bound as the distortion parameter varies. In the limit as the distortion tolerated goes to zero, the conditional density achieving the rate distortion function lower bound becomes degenerate in the sense that the channel it defines becomes error-free. As the permitted di... View full abstract»

• ### Binary sequences with two-level autocorrelation

Publication Year: 1999, Page(s):692 - 693
Cited by:  Papers (9)
| |PDF (104 KB)

We derive the values of the Fourier spectrum, a decomposition, and an achievable upper bound on the linear span, for binary sequences with two-level autocorrelation View full abstract»

• ### Cyclotomy and duadic codes of prime lengths

Publication Year: 1999, Page(s):453 - 466
Cited by:  Papers (15)
| |PDF (620 KB)

We present a cyclotomic approach to the construction of all binary duadic codes of prime lengths. We calculate the number of all binary duadic codes for a given prime length and that of all duadic codes that are not quadratic residue codes. We give necessary and sufficient conditions for p such that all binary duadic codes of length p are quadratic residue (QR) codes. We also show how to determine... View full abstract»

• ### Codes on Garcia-Stichtenoth curves with true distance greater than Feng-Rao distance

Publication Year: 1999, Page(s):706 - 709
Cited by:  Papers (6)
| |PDF (172 KB)

We give codes on all members after level 4 of the family of Garcia-Stichtenoth (see Invent. Math., vol.121, p.211-22, 1995) curves with the property dtrue>dFR. These codes also give an improvement on Tsfasman-Vladut-Zink bound View full abstract»

• ### Constructions of generalized concatenated codes and their trellis-based decoding complexity

Publication Year: 1999, Page(s):725 - 731
Cited by:  Papers (3)
| |PDF (288 KB)

In this article, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis complexity than Euclidean geometry (EG), Reed-Muller (RM), or Bose-Chaudhuri-Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to th... View full abstract»

• ### Correlation attacks on up/down and stop/go cascades

Publication Year: 1999, Page(s):486 - 498
Cited by:  Papers (2)
| |PDF (548 KB)

A probabilistic analysis is conducted to determine conditional and unconditional correlation weaknesses of cascades of up/down clocked shift registers. Similar results are also obtained for cascades of stop/go clocked shift registers. It is theoretically explained how to use the derived properties for fast correlation attacks, whose objective is to recover the linear feedback shift-register initia... View full abstract»

• ### Noise conditions for prespecified convergence rates of stochastic approximation algorithms

Publication Year: 1999, Page(s):810 - 814
Cited by:  Papers (8)
| |PDF (212 KB)

We develop deterministic necessary and sufficient conditions on individual noise sequences of a stochastic approximation algorithm for the error of the iterates to converge at a given rate. Specifically, suppose {ρn} is a given positive sequence converging monotonically to zero. Consider a stochastic approximation algorithm x n+1=xn-an(Anx... View full abstract»

• ### An improved upper bound of the rate of Euclidean superimposed codes

Publication Year: 1999, Page(s):799 - 802
Cited by:  Papers (7)
| |PDF (184 KB)

A family of n-dimensional unit norm vectors is an Euclidean superimposed code if the sums of any two distinct at most m-tuples of vectors are separated by a certain minimum Euclidean distance d. Ericson and Gyorfi (1988) proved that the rate of such a code is between (log m)/4m and (log m)/m for m large enough. In this paper-improving the above long-standing best upper bound for the rate-it is sho... View full abstract»

• ### High-resolution source coding for non-difference distortion measures: multidimensional companding

Publication Year: 1999, Page(s):548 - 561
Cited by:  Papers (37)
| |PDF (736 KB)

Entropy-coded vector quantization is studied using high-resolution multidimensional companding over a class of nondifference distortion measures. For distortion measures which are “locally quadratic” a rigorous derivation of the asymptotic distortion and entropy-coded rate of multidimensional companders is given along with conditions for the optimal choice of the compressor function. T... View full abstract»

• ### Improved rates and asymptotic normality for nonparametric neural network estimators

Publication Year: 1999, Page(s):682 - 691
Cited by:  Papers (27)
| |PDF (580 KB)

We obtain an improved approximation rate (in Sobolev norm) of r -1/2-α(d+1)/ for a large class of single hidden layer feedforward artificial neural networks (ANN) with r hidden units and possibly nonsigmoid activation functions when the target function satisfies certain smoothness conditions. Here, d is the dimension of the domain of the target function, and α∈(0, 1) is... View full abstract»

• ### Trellis-coded quantization for binary erasure channels

Publication Year: 1999, Page(s):781 - 787
Cited by:  Papers (1)
| |PDF (272 KB)

Trellis-coded quantizers (TCQ) are designed for the binary erasure channel (BEC) for memoryless sources. When the bit erasure rate is large, the channel-optimized TCQ can provide up to 1.4 dB improvement over TCQ designed for a lossless channel View full abstract»

• ### Binomial moments of the distance distribution: bounds and applications

Publication Year: 1999, Page(s):438 - 452
Cited by:  Papers (25)
| |PDF (748 KB)

We study a combinatorial invariant of codes which counts the number of ordered pairs of codewords in all subcodes of restricted support in a code. This invariant can be expressed as a linear form of the components of the distance distribution of the code with binomial numbers as coefficients. For this reason we call it a binomial moment of the distance distribution. Binomial moments appear in the ... View full abstract»

• ### Codes of lengths 120 and 136 meeting the Grey-Rankin bound and quasi-symmetric designs

Publication Year: 1999, Page(s):703 - 706
Cited by:  Papers (2)
| |PDF (188 KB)

In this correspondence, we give a characterization of certain quasi-cyclic self-complementary codes with parameters [120,9,56] and [136,9,64], some quasi-cyclic self-complementary codes are also constructed with parameters [496,11,240] and [528,11,256]. These codes are optimal in the sense that they meet the Grey-Rankin bound, new quasi-symmetric SDP (symmetric difference property) designs are con... View full abstract»

• ### On symmetrical multilevel diversity coding

Publication Year: 1999, Page(s):609 - 621
Cited by:  Papers (47)
| |PDF (924 KB)

Symmetrical multilevel diversity coding with independent data streams has been studied by Roche et al. (1992), and the admissible coding rate region was determined for the case of three levels. In particular, it was shown that coding by superposition is optimal, which means that optimality can be achieved by very simple coding. However, it is very difficult to generalize their proof to an arbitrar... View full abstract»

• ### On the rectangularity of nonlinear block codes

Publication Year: 1999, Page(s):720 - 725
Cited by:  Papers (2)
| |PDF (228 KB)

We give simple sufficient conditions for a code to be rectangular and show that large families of well-known nonlinear codes are rectangular. These include Hadamard (1893), Levenshtein (1964), Delsarte-Goethals (1975), Kerdock (1972), and Nordstrom-Robinson (1967) codes. Being rectangular, each of these codes has a unique minimal trellis that can be used for soft-decision maximum-likelihood decodi... View full abstract»

• ### New families of almost perfect nonlinear power mappings

Publication Year: 1999, Page(s):475 - 485
Cited by:  Papers (40)
| |PDF (600 KB)

A power mapping f(x)=xd over GF(pn) is said to be differentially k-uniform if k is the maximum number of solutions x∈GF(pn) of f(x+a)-f(x)=b where a, b∈GF(pn ) and a≠0. A 2-uniform mapping is called almost perfect nonlinear (APN). We construct several new infinite families of nonbinary APN power mappings View full abstract»

• ### Arbitrarily varying multiple-access channels. I. Ericson's symmetrizability is adequate, Gubner's conjecture is true

Publication Year: 1999, Page(s):742 - 749
Cited by:  Papers (19)
| |PDF (436 KB)

In 1981 Jahn used the elimination technique of the first author to determine the average errors capacity region of an arbitrarily varying multiple-access channel (AVMAC), when this region has a nonempty interior. Here we remove this restriction. In his thesis (1990), Gubner (1990) missed this result because he used the first author's first approach to the MAC, which is based on conditional decodin... View full abstract»

• ### Note on taking square-roots modulo N

Publication Year: 1999, Page(s):807 - 809
Cited by:  Papers (1)  |  Patents (2)
| |PDF (116 KB)

In this article it is shown how Gauss' (1981) famous cyclotomic sum formula can be used for extracting square-roots modulo N View full abstract»

• ### Efficient code constructions for certain two-dimensional constraints

Publication Year: 1999, Page(s):794 - 799
Cited by:  Papers (20)  |  Patents (2)
| |PDF (232 KB)

Efficient encoding algorithms are presented for two types of constraints on two-dimensional binary arrays. The first constraint considered is that of t-conservative arrays, where each row and each column has at least t transitions of the form 0'→1' or 1'→0.' The second constraint is that of two-dimensional DC-free arrays, where in each row and each column the number of `0's equals th... View full abstract»

• ### High-resolution source coding for non-difference distortion measures: the rate-distortion function

Publication Year: 1999, Page(s):533 - 547
Cited by:  Papers (15)
| |PDF (952 KB)

The problem of asymptotic (i,e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x,y)=||W(x)(y-x)||2... View full abstract»

## Aims & Scope

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

Full Aims & Scope

## Meet Our Editors

Editor-in-Chief
Prakash Narayan

Department of Electrical and Computer Engineering