In this paper, we study cyclic codes over the ring Z p + uZ p + · · · + u k−1 Z p , where u k = 0. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.

We describe the defining sets of extended cyclic codes of length pn over a field and over the ring of integers modulo pe admitting the affine group AGLm(p ), n=mt , as a permutation group. © 2004 Elsevier B.V. All rights reserved. MSC: 94B05; 20B25; 94B15; 94B60

In this paper, a family of cyclic codes over Fp whose duals have five zeros is presented, where p is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

In this article, we study skew cyclic codes over ring R = Fq + vFq + v 2 Fq, where q = p, p is an odd prime and v3 = v. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent genera...

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.

Abstract. BinaryWhiteman’s cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman’s generalized cyclotomic sequence (WGCS-I) of order d = 6. Our results show that the autocorrelation values of this sequence is four-valued or five-valued if (n1−1)(n2−1)/36...

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...

An [18,9,8] code Ce18 over GF(4) was constructed in [6] as an extended cyclic code, and Pless [9] describes the same code as an extended “Q-code”. This code is of particular interest since it is an extremal quaternary code: an [n, n/2, d] self-dual code with d = 2[n/6] + 2 ([6, p. 2951, [3, p. 2051). In the present note we give new coordinates for this code, enabling us to find a simple descrip...

This paper develops a constant amortized time algorithm to produce the cyclic cool-lex Gray code for fixed-density binary necklaces, Lyndon words, and pseudo-necklaces. It is the first Gray code for these objects that achieves this time bound. In addition to Gray code order, the algorithms can be easily modified to output the strings in co-lex order.

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over ...