22 research outputs found

    Constacyclic Codes over Finite Fields

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    An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length β„“tps\ell^tp^s are characterized, where pp is the characteristic of the finite field and β„“\ell is a prime different from pp

    Recent progress on weight distributions of cyclic codes over finite fields

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    Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions

    Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

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    Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p^a,m) and generating sets for its ideals are considered. Along with some structure details of the ambient ring, the existance of a certain type of generating set for an ideal is proven.Comment: arXiv admin note: text overlap with arXiv:0906.400
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