Flash memory is a nonvolatile memory technology that suffers from errors due to charge leakage, can tolerate limited erasures, and where erasures have to be performed in large blocks. We show that using cosets of a linear code can provide correction against uniform charge leakage, and can enhance the rewritability of flash memory which leads to fewer erasures. We introduce two coset coding schemes that are generalizations of the scheme in Jacobvitz et al. (2013). For the same worst case rewrite cost, we show that coset codes can encode more information than rank modulation codes. The average case performance of coset codes is demonstrated via numerical simulations.

Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of binary linear codes. Additionally, the constructions have the property that they are systematic. Subsequently, we generalize our construction to irregular product of affine codes, where the component codes are affine codes of different rates.

Single-tone frequency shift keying (FSK) modulation with permutation codes has been found to be useful in addressing the problem of narrowband noise disturbance in power line communications. However, this modulation scheme is restrictive since the number of frequencies used must be at least as large as the number of symbols in the permutation code. In this paper, we propose the use of multitone FSK and binary matrix codes to overcome this restriction. We construct infinite families of efficiently decodable matrix codes with rates and relative distances bounded away from zero, that uses only a logarithmic number of frequencies in the length of the code. Simulation results show that our multitone modulation scheme outperform single-tone modulation schemes.

The use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system. In this paper, we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that more precisely captures a code's performance against permanent narrowband noise. As a result, we define a new class of codes, namely, equitable symbol weight codes, which are optimal with respect to this measure.

The study of codes for powerline communications has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the years. In this paper, we study a type of code called bounded symbol weight codes which was first introduced by Versfeld in 2005, and a related family of codes that we term constant symbol weight codes. We provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes. We also give direct and recursive constructions of codes for certain parameters.

A cross-bifix-free code is a set of words in which no prefix of any length of any word is the suffix of any word in the set. Cross-bifix-free codes arise in the study of distributed sequences for frame synchronization. We provide a new construction of cross-bifix-free codes which generalizes the construction by Bajic to longer code lengths and to any alphabet size. The codes are shown to be nearly optimal in size. We also establish new results on Fibonacci sequences, which are used in estimating the size of the cross-bifix-free codes.

In this article we construct an infinite family of linear error correcting codes over Fqfor any prime power q. The code parameters are [q2t+ qt-1- q2t-1- qt, 2t+1, q2t+ q2t-2+ qt-1- 2q2t-1- qt]q, for any positive integer t. This family is a generalisation of the optimal self-complementary binary codes with parameters [2u2- u, 2t + 1, u2- u]2, where u = 2t-1. The codes are obtained by considering a submatrix of a specially constructed generalised Hadamard matrix. The optimality of the family is confirmed by using a recently derived generalisation of the Grey-Rankin bound when t >; 1, and the Griesmer bound when t = 1.

The use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system. In this paper, we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that helps to more precisely capture a code's performance against permanent narrowband noise. As a result, we define a new class of codes, namely, equitable symbol weight codes, which are optimal with respect to this measure. In addition, we demonstrate via simulations that equitable symbol weight codes achieve lower symbol error rates than other codes of the same length and distance over the same alphabet.

We study the decoding of permutation codes obtained from distance preserving maps and distance increasing maps from Hamming space. We provide efficient algorithms for estimating the q-ary digits of the Hamming space so that decoding can be performed in the Hamming space.

We study q-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close to MDS codes by the value of their minimum distance. For such codes, we determine their weight distribution, and in the particular case of the “ordered metric” characterize distributions of points in the unit cube defined by the codes. We also give some constructions of codes in the ordered Hamming space.

We prove several new bounds on ordered codes and ordered orthogonal arrays. We also show that the eigenvalues of the ordered Hamming scheme are the multivariable Krawtchouk polynomials and establish some of their properties.