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Codes with girth 8 Tanner graph representation

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Abstract

Since short cycles are (empirically) detrimental to message passing, determining the girth of a given code is of interest in coding theory. Halford et al. studied codes which do not have a 4-cycle-free Tanner graph representation. It is natural to then ask which codes must have girth 8. In this paper, a new necessary condition is derived for codes to have girth 8. Halford et al. made statements about the girth of high rate well known codes but the girth of lower rate codes remain open. In this work, we investigate girth of low rate Reed–Muller, BCH and Reed–Solomon codes.

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Correspondence to Mohammad-Reza Sadeghi.

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Communicated by T. Helleseth.

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Sakzad, A., Sadeghi, MR. & Panario, D. Codes with girth 8 Tanner graph representation. Des. Codes Cryptogr. 57, 71–81 (2010). https://doi.org/10.1007/s10623-009-9349-0

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  • DOI: https://doi.org/10.1007/s10623-009-9349-0

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