Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance

  • Authors:

  • E. Cadic;Jean-Claude Carlach;G. Olocco;A. Otmani;Jean-Pierre Tillich

  • Affiliations:

  • -;-;-;-;-

  • Venue:
  • AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
  • Year:
  • 2001

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Abstract

We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24, 12, 8] Golay code, and two extremal self-dual codes with parameters [32, 16, 8] and [40, 20, 8] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and [32, 16, 12] by using the [8, 4, 6] octacode. Moreover, there is a natural Tanner graph associated to the construction of [3], and it turns out that all our constructions have Tanner graphs that have a cyclic structure which gives tail-biting trellises of low complexity: 16-state tail-biting trellises for the [24, 12, 8], [32, 16, 8], [40, 20, 8] binary codes, and 256-state tail-biting trellises for the [24, 12, 12] and [32, 16, 12] codes over Z4.