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Optimal ternary quasi-cyclic codes

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Abstract

Quasi-cyclic codes have provided a rich source of good linear codes. Previous constructions of quasi-cyclic codes have been confined mainly to codes whose length is a multiple of the dimension. In this paper it is shown how searches may be extended to codes whose length is a multiple of some integer which is greater than the dimension. The particular case of 5-dimensional codes over GF(3) is considered and a number of optimal codes (i.e., [n, k, d]-codes having largest possible minimum distance d for given length n and dimension k) are constructed. These include ternary codes with parameters [45, 5, 28], [36, 5, 22], [42, 5, 26], [48, 5, 30] and [72, 5, 46], all of which improve on the previously best known bounds.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Salford, M5 4WT, Salford, UK

    P. P. Greenough & R. Hill

Authors
  1. P. P. Greenough
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  2. R. Hill
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Additional information

Communicated by H. van Tilborg

This research has been supported by the British SERC.

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Greenough, P.P., Hill, R. Optimal ternary quasi-cyclic codes. Des Codes Crypt 2, 81–91 (1992). https://doi.org/10.1007/BF00124211

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  • DOI: https://doi.org/10.1007/BF00124211

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