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Maximum-distance-separable (MDS) codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field F q has been completely solved for q is even. In this paper, for finite field with odd characteristic, we obtain some new results on the existence of MDS self-dual codes by generalized Reed-Solomon (GRS) codes and extended GRS codes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we explore constacyclic self-dual codes over . We first characterize constacyclic self-dual codes over of any length. Then we determine the structure of η-constacyclic self-dual codes over , where or . This structure is used to find some constacyclic self-dual codes over . [Copyright &y& Elsevier]

Abstract: We study -constacyclic codes over of an arbitrary length, where λ is a unit of and is a positive integer. We first derive the structure of -constacyclic codes of length over and determine the Hamming and homogeneous distances of such constacyclic codes. These codes are then used to classify all -constacyclic codes over of length (n prime to p). In particular, the Gray images of -constacyclic codes over are also discussed. [Copyright &y& Elsevier]

Abstract We investigate the minimum distance of q -ary negacyclic codes of length q m − 1 2 generated by a product of two distinct minimal polynomials. A necessary and sufficient condition on the minimum distance of such negacyclic codes is given. Several classes of optimal quinary negacyclic codes with parameters [ (5 m − 1) / 2 , (5 m − 1) / 2 − 2 m , 4 ] are constructed. The dual codes of a subclass of the quinary negacyclic codes are studied. A comparison with cyclic codes is also presented. [ABSTRACT FROM AUTHOR]

Any permutation polynomial is an n -cycle permutation. When n is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These permutations have important applications in cryptography and coding theory. Inspired by the AGW Criterion, we propose criteria for n -cycle permutations, which mainly are of the form x r h (x s). We then propose unified constructing methods including recursive ways and a cyclotomic way for n -cycle permutations of such form. We demonstrate our approaches by constructing three classes of explicit triple-cycle permutations with high index and two classes of n -cycle permutations with low index, many of which are new both at levels of permutation property and cycle property. [ABSTRACT FROM AUTHOR]