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On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings

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Abstract

The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech lattice is derived.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore, 117543

    San Ling

  2. CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903, Sophia Antipolis, France

    Patrick Solé

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  1. San Ling
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Ling, S., Solé, P. On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings. Designs, Codes and Cryptography 30, 113–130 (2003). https://doi.org/10.1023/A:1024715527805

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