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Decomposing Quasi-Cyclic Codes

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Abstract

A new algebraic approach to quasi-cyclic codes is introduced. Technical tools include the Chinese Remainder Theorem, the Discrete Fourier Transform, Chain rings. The main results are a characterization of self-dual quasi-cyclic codes, a trace representation that generalizes that of cyclic codes, and an interpretation of the squaring and cubing construction (and of several similar combinatorial constructions). All extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction. Quinting and septing constructions are introduced.

References (20)

  • V. Pless

    Symmetry codes over GF (3) and new 5-designs

    J. Comb. Theory

    (1972)
  • Y. Berger et al.

    The twisted squaring construction trellis complexity, and generalized weights of BCH and QR codes

    IEEE Trans. Inform. Theory

    (1996)
  • A. Bonnecaze et al.

    Quaternary quadratic residue codes and unimodular lattices

    IEEE Trans. Inform. Theory

    (1995)
  • Z. Chen,...
  • J. Conan et al.

    Structural properties and enumeration of quasi-cyclic codes

    AAECC

    (1993)
  • S.T. Dougherty et al.

    Type II codes over F2 + uF2

    IEEE Trans. Inform. Theory

    (1999)
  • W. Feit

    A self-dual even (96, 48, 16) code

    IEEE Trans. Inform. Theory

    (1974)
  • G.D. Forney

    Coset codes II: binary lattices

    IEEE Trans. Inform. Theory

    (1988)
  • W.C. Huffman

    Codes and groups

There are more references available in the full text version of this article.

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1

This work was done was the first named author was visiting CNRS-I3S, ESSI, Sophia Antipolis, France. The author would like to thank the institution for the kind hospitality. The research of this author is partially supported by MOE-ARF research grant R-146-000-018-112.

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