Abstract
In this article, some row-cyclic error-correcting codes are shown to be ideals in group rings in which the underlying group is metacyclic. For a given underlying group, several nonequivalent codes with this structure may be generated. Each is related to a cyclic code generated in response, to the metrics associated with the underlying metacyclic group. Such codes in the same group ring are isomorphic as vector spaces but may vary greatly in weight distributions and so are nonequivalent. If the associated cyclic code is irreducible, examining the structure of its isomorphic finite field yields all nonequivalent codes with the desired structure. Several such codes have been found to have minimum distances equalling those of the best known linear codes of the same length and dimension.
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Communicated by S. Vanstone
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Sabin, R.E. On row-cyclic codes with algebraic structure. Des Codes Crypt 4, 145–155 (1994). https://doi.org/10.1007/BF01578868
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DOI: https://doi.org/10.1007/BF01578868