Codes with girth 8 Tanner graph representation

Authors:
Amin Sakzad;Mohammad-Reza Sadeghi;Daniel Panario
Affiliations:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran;Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran;School of Mathematics and Statistics, Carleton University, Ottawa, Canada
Venue:
Designs, Codes and Cryptography
Year:
2010

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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.