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# IEEE Transactions on Information Theory

## Volume 64 Issue 4  Part 2 • April 2018

This issue contains several parts.Go to:  Part 1

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## Filter Results

Displaying Results 1 - 25 of 40

Publication Year: 2018, Page(s):C1 - C4
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• ### IEEE Transactions on Information Theory publication information

Publication Year: 2018, Page(s): C2
| PDF (66 KB)
• ### A Career in Engineering

Publication Year: 2018, Page(s):2805 - 2836
| | PDF (9475 KB) | HTML

During the summers (1951-1954) that I was a graduate student in “pure mathematics,” I worked in the Systems Engineering Section of the Glenn L. Martin Company. I began to notice the applicability of supposedly pure topics like prime number theory and finite field theory to problems in communications. My first major applied effort involved developing the theory of “Shift Regist... View full abstract»

• ### Solomon Wolf Golomb 1932–2016

Publication Year: 2018, Page(s):2837 - 2838
| PDF (66 KB) | HTML
• ### Puzzles in Memory of Solomon Golomb

Publication Year: 2018, Page(s):2839 - 2843
| | PDF (241 KB) | HTML

We give 12 mathematical puzzles (and their solutions) that were presented at a special session in honor of Sol Golomb at the 2017 ITA meeting in San Diego. Some are “well known,” and the very first one is a famous result due to Golomb. View full abstract»

• ### Solomon W. Golomb—Mathematician, Engineer, and Pioneer

Publication Year: 2018, Page(s):2844 - 2857
| | PDF (1878 KB) | HTML

In this paper, we present some fundamental concepts and theoretical advances attributable to Solomon Golomb, together with the history and applications of this paper to communications, coding, and cryptography, along with some long-standing conjectures. Examples include the first engineering problem relating to feedback shift-register sequences that Sol Golomb was asked to solve in the mid-1950s. ... View full abstract»

• ### Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions

Publication Year: 2018, Page(s):2858 - 2875
| | PDF (623 KB) | HTML

The design of code division multiple access sequence families dates back to the Gold sequences from the 1960s. Since then there has been a number of different such designs with good correlation properties, some optimal and some near-optimal. In this paper, we use the concept of plateaued functions with arbitrary degree, in order to compute their full correlation distributions. First, we give an ex... View full abstract»

• ### Optimum Sets of Interference-Free Sequences With Zero Autocorrelation Zones

Publication Year: 2018, Page(s):2876 - 2882
| | PDF (287 KB) | HTML

A general construction of a particular class of zero correlation zone sequences is proposed. The general construction produces the sets of so-called interference-free zero autocorrelation zone (IF-ZAZ) sequences, where any two sequences from a set have all-zero periodic cross correlation, while each sequence has periodic autocorrelation equal to zero in multiple zones of non-zero delays. The lengt... View full abstract»

• ### Geometric Orthogonal Codes of Size Larger Than Optical Orthogonal Codes

Publication Year: 2018, Page(s):2883 - 2895
| | PDF (1606 KB) | HTML

The class of geometric orthogonal codes (GOCs) was introduced by Doty and Winslow (2016) for more robust macrobonding in DNA origami. They observed that GOCs are closely related to optical orthogonal codes (OOCs). It is possible for GOCs to have size greater than OOCs of corresponding parameters due to slightly more relaxed constraints on correlations. However, the existence of GOCs exceeding the ... View full abstract»

• ### A Family of Polyphase Sequences With Asymptotically Optimal Correlation

Publication Year: 2018, Page(s):2896 - 2900
| | PDF (385 KB) | HTML

Sequences with low correlation have important applications in communications, radar, and cryptography. In this paper, a simple construction of polyphase sequences using additive and multiplicative characters over the finite field Fq is proposed. The construction works for any finite field Fq with q > 2 and generates a family of q - 1 sequences with period q - 1 and maximum... View full abstract»

• ### A Construction of Odd Length Generators for Optimal Families of Perfect Sequences

Publication Year: 2018, Page(s):2901 - 2909
| | PDF (607 KB) | HTML

In this paper, we give a construction of optimal families of N-ary perfect sequences of period N2, where N is a positive odd integer. For this, we re-define perfect generators and optimal generators of any length N which were originally defined only for odd prime lengths by Park, Song, Kim, and Golomb in 2016, but investigate the necessary and sufficient condition for these generators f... View full abstract»

• ### CRT Sequences With Applications to Collision Channels Allowing Successive Interference Cancellation

Publication Year: 2018, Page(s):2910 - 2923
| | PDF (938 KB) | HTML

Protocol sequences are periodic zero-one sequences for the scheduling of packet transmissions in a time-slotted channel. A special class of protocol sequences, called shift-invariant sequences, plays a key role in achieving the information-theoretic capacity of the collision channel without feedback. This class of shift-invariant protocol sequences has the property that the pairwise Hamming crossc... View full abstract»

• ### Sequence Reconstruction Over the Deletion Channel

Publication Year: 2018, Page(s):2924 - 2931
| | PDF (310 KB) | HTML

The sequence reconstruction problem, first proposed by Levenshtein, models the setup in which a sequence from some set is transmitted over several channels, and the decoder receives the outputs from every channel. The channels are almost independent as it is only required that all outputs are different from each other. The main problem of interest is to determine the minimum number of channels req... View full abstract»

• ### On the Affine Sub-Families of Quadratic NFSRs

Publication Year: 2018, Page(s):2932 - 2940
| | PDF (297 KB) | HTML

Grain-128 is a hardware oriented stream cipher based on the cascade connection of a 128-bit linear feedback shift register into a 128-bit quadratic nonlinear feedback shift register (NFSR). Its main register is in essence a quadratic NFSR, however its affine sub-families could not be solved by the previous methods. In this paper, it is shown that the family of sequences generated by the main regis... View full abstract»

• ### De Bruijn Sequences, Adjacency Graphs, and Cyclotomy

Publication Year: 2018, Page(s):2941 - 2952
| | PDF (734 KB) | HTML

We study the problem of constructing De Bruijn sequences by joining cycles of linear feedback shift registers (LFSRs) with reducible characteristic polynomials. The main difficulty for joining cycles is to find the location of conjugate pairs between cycles, and the distribution of conjugate pairs in cycles is defined to be adjacency graphs. Let l(x) be a characteristic polynomial, and l(x) = l View full abstract»

• ### On the Nonexistence of $q$ -Bent Boolean Functions

Publication Year: 2018, Page(s):2953 - 2961
| | PDF (239 KB) | HTML

We continue the study of the properties of Boolean functions as reflected in The properties of a recently defined transform. For each non-constant Boolean function q, the q-transform of a Boolean function f is related to the Hamming distances from f to the functions obtainable from q by nonsingular linear change of basis. Many properties that can be characterized by the Walsh-Hadamard transform ha... View full abstract»

• ### Weight Recursions for Any Rotation Symmetric Boolean Functions

Publication Year: 2018, Page(s):2962 - 2968
| | PDF (229 KB) | HTML

Let fn(x1, x2,⋯, xn) denote the algebraic normal form (polynomial form) of a rotation symmetric Boolean function of degree d in n ≥ d variables and let wt(fn) denote the Hamming weight of this function. Let (1, α2,⋯, αd)n denote the function fn of degree ... View full abstract»

• ### Constructing Low-Weight $d$ th-Order Correlation-Immune Boolean Functions Through the Fourier-Hadamard Transform

Publication Year: 2018, Page(s):2969 - 2978
| | PDF (412 KB) | HTML

The correlation immunity of Boolean functions is a property related to cryptography, to error correcting codes, to orthogonal arrays (in combinatorics), and in a slightly looser way to sequences. Correlation-immune Boolean functions (in short, CI functions) have the property of keeping the same output distribution when some input variables are fixed. They have been widely used as combiners in stre... View full abstract»

• ### Bent Functions From Involutions Over ${mathbb F}_{2^{n}}$

Publication Year: 2018, Page(s):2979 - 2986
| | PDF (244 KB) | HTML

Bent functions are maximally nonlinear Boolean functions. Introduced by Rothaus and first examined by Dillon, these important functions have subsequently been studied by many researchers over the last four decades. Since a complete classification of bent functions appears elusive, many researchers concentrate on methods for constructing bent functions. In this paper, we investigate constructions o... View full abstract»

• ### Large Sets of Disjoint Spectra Plateaued Functions Inequivalent to Partially Linear Functions

Publication Year: 2018, Page(s):2987 - 2999
| | PDF (553 KB) | HTML

In this paper, we give an efficient method for constructing a large set of disjoint spectra functions without linear structures, which are not equivalent to partially linear functions. This positively answers the open problem [“how to construct a large set of disjoint spectra functions which are not (linearly equivalent to) partially linear functions” raised by Zhang and Xiao]. At th... View full abstract»

• ### Discrete Fourier Transform of Boolean Functions over the Complex Field and Its Applications

Publication Year: 2018, Page(s):3000 - 3009
| | PDF (263 KB) | HTML

In this paper, the discrete Fourier transform (DFT) of Boolean functions over the complex field is introduced and the locations of zero-valued Fourier spectrum are studied. Then a Fourier spectral characterization of correlation immune and resilient Boolean functions is investigated. It is shown that a Boolean function f is mth-order correlation immune if and only if the Fourier spectrum of f unde... View full abstract»

• ### Linear Codes Over $mathbb F_q$ Are Equivalent to LCD Codes for $q>3$

Publication Year: 2018, Page(s):3010 - 3017
| | PDF (246 KB) | HTML

Linear codes with complementary duals (LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Nonbinary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. In this paper, we introduce a general construction of LCD co... View full abstract»

• ### Rate $(n-1)/n$ Systematic Memory Maximum Distance Separable Convolutional Codes

Publication Year: 2018, Page(s):3018 - 3030
| | PDF (1483 KB) | HTML

A systematic convolutional encoder of rate (n-1)/n and maximum memory D generates a code of free distance at most V = D + 2 and, at best, a column distance profile (CDP) of [2,3, .. . , D]. A code is memory maximum distance separable if it possesses this CDP. Applied on a communication channel over which packets are transmitted sequentially and which loses (erases) packets randomly, such a code al... View full abstract»

• ### 2-Correcting Lee Codes: (Quasi)-Perfect Spectral Conditions and Some Constructions

Publication Year: 2018, Page(s):3031 - 3041
| | PDF (284 KB) | HTML

Let p be an odd prime. Recently, Camarero and Martínez (in “Quasi-perfect Lee codes of radius 2 and arbitrarily large dimension”, IEEE Trans. Inform. Theory, vol. 62, no. 3, 2016) constructed some p-ary 2-quasi-perfect Lee codes for p ≡ ±5 (mod 12). In this paper, some infinite classes of p-ary 2-quasi-perfect Lee codes for any odd prime p with flexible length a... View full abstract»

• ### Non-Existence of Linear Perfect Lee Codes With Radius 2 for Infinitely Many Dimensions

Publication Year: 2018, Page(s):3042 - 3047
| | PDF (447 KB) | HTML

The Golomb-Welch conjecture (1968) on the non-existence of perfect Lee codes in Zn with radius e ≥ 2 and dimensions n ≥ 3, widely believed to be true, has been up to now only proved for large radius in any dimension, for small dimensions, and for some small radii and specific n. The main result of this paper is that for radius e = 2, there are no perfect Lee linear codes i... 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