Abstract
We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] 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.
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Cadic, E., Carlach, J., Olocco, G., Otmani, A., Tillich, J. (2001). Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_6
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DOI: https://doi.org/10.1007/3-540-45624-4_6
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