An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear codes, which are binary and, in general, nonlinear codes in the usual sense. For this, it is proved that these codes allow a systematic encoding scheme. As a ...

Permutation decoding is a technique that strongly depends on the existence of a special subset, called PD-set, of the permutation automorphism group of a code. In this paper, a general criterion to obtain s-PD-sets of size s + 1, which enable correction up to s errors, for Z4-linear codes is provided. Furthermore, some explicit constructions of s-PD-sets of size s+1 for important families of (n...

This paper addresses two coding schemes which can handle emerging errors with crisscross patterns. First, a code with maximum rank distance, so-called Rank-Codes, is described and a modified Berlekamp-Massey algorithm is provided. Secondly, a Permutation Code based coding scheme for crisscross error patterns is presented. The influence of different types of noise are also discussed.

We cryptanalyse here two variants of the McEliece cryptosystem based on quasi-cyclic codes. Both aim at reducing the key size by restricting the public and secret generator matrices to be in quasi-cyclic form. The first variant considers subcodes of a primitive BCH code. The aforementioned constraint on the public and secret keys implies to choose very structured permutations. We prove that thi...

Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient condition that determines the least degree inverse of a quadratic permutation polynomial is proven. Moreover, an algorithm is provided to explicitly compute th...

An algorithm for generating parity-check matrices of high-rate lowdensity parity-check codes based on permutation matrices and Steiner system S(v, 4, 2) is proposed. The estimations of rate, minimum distance and girth for derived code constructions are presented. The results of simulation of obtained code constructions for an iterative ”belief propagation” (Sum-Product) decoding algorithm, appl...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

Permutation codes, introduced by Slepian, were shown to perform well on an additive white Gaussian noise (AWGN) channel. Unfortunately, these codes required large lookup tables, making them quite complex to implement even though the maximum-likelihood decoder is very simple. In this correspondence, we present an enumeration scheme which encodes and decodes permutation codes with low complexity....

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T (n) for any n ≥ 5.