Let S = GR(p(e), m) be a Galois ring of characteristic p(e) and cardinality p(em). An additive code over S of length n is a subgroup of S-n under addition. In this paper, we study additive codes over S. We introduce a...
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Let S = GR(p(e), m) be a Galois ring of characteristic p(e) and cardinality p(em). An additive code over S of length n is a subgroup of S-n under addition. In this paper, we study additive codes over S. We introduce a correspondence between linear codes over Z(pe) and additive codes over S and we describe additive codes over S by the structure of linear codes over Z(pe). In particular, we find the generator matrix and the number of additive codes over S, and we determine some classes of mdr additive codes over S. Among other results, permutation equivalent additive codes and decomposable additive codes are described. Also we prove MacWilliams identity and Delsarte theorem for additive codes over S. (C) 2018 Published by Elsevier Inc.
In this article, we study negacyclic self-dual codes of length n over a finite chain ring R when the characteristic p of the residue field (R) over bar and the length n are relatively prime. We give necessary and suff...
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In this article, we study negacyclic self-dual codes of length n over a finite chain ring R when the characteristic p of the residue field (R) over bar and the length n are relatively prime. We give necessary and sufficient conditions for the existence of (nontrivial) negacyclic self-dual codes over a finite chain ring. As an application, we construct negacyclic mdr self-dual codes over GR(p (t) , m) of length p (m) + 1.
We study alpha-constacyclic codes over the Frobenius non-chain ring R := Z(4)[u]/ for any unit alpha of R. We obtain new mdr cyclic codes over Z(4) using a close connection between alpha-constacyclic codes over R and ...
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We study alpha-constacyclic codes over the Frobenius non-chain ring R := Z(4)[u]/< u(2) - 1 > for any unit alpha of R. We obtain new mdr cyclic codes over Z(4) using a close connection between alpha-constacyclic codes over R and cyclic codes over Z(4). We first explicitly determine generators of all alpha-constacyclic codes over R of odd length n for any unit alpha of R. We then explicitly obtain generators of cyclic codes over Z(4) of length 2n by using a Gray map associated with the unit alpha. This leads to a construction of infinite families of mdr cyclic codes over Z(4), where a mdr code means a maximum distance with respect to rank code in terms of the Hamming weight or the Lee weight. We obtain 202 new cyclic codes over Z(4) of lengths 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50 and 54 by implementing our results in Magma software;some of them are also mdr codes with respect to the Hamming weight or the Lee weight. (C) 2019 Elsevier B.V. All rights reserved.
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