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Hartmann--Tzeng bound and Skew Cyclic Codes of Designed Hamming Distance | | José Gómez-Torrecillas
; Gabriel Navarro
; F.J. Lobillo
; Alessandro Neri
; | | Date: |
9 Nov 2017 | | Abstract: | The use of skew polynomial rings allows to endow linear codes with cyclic
structures which are not cyclic in the classical (commutative) sense. Whenever
these skew cyclic structures are carefully chosen, some control over the
Hamming distance is gained, and it is possible to design efficient decoding
algorithms. In this paper, we give a version of the Hartmann-Tzeng bound that
works for a wide class of skew cyclic codes. We also provide a practical method
for constructing them with designed distance. For skew BCH codes, which are
covered by our constructions, we discuss decoding algorithms. Detailed examples
illustrate both the theory as the constructive methods it supports. | | Source: | arXiv, 1711.3515 | | Services: | Forum | Review | PDF | Favorites | |
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