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Majority-logic-decodable cyclic arithmetic-modular AN-codes in 1, 2, and L steps

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Abstract

We generalize to any base r ≥ 2 the Majority-Logic-Decodification Algorithms already considered for r = 2 by Chin-Long Chen, Robert T. Chien and Chao-Kai Liu [2]. The codes considered are generated by ϕn(r) where ϕn(x) is the nth-cyclotomic polynomial associated to the polynomial xn−1. Hong Decodification Algorithm [7] is also applicable to these codes, but achieves quite higher computational complexity.

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Javier Galán-Simón, F., Martínez-Moro, E., & Tena-Ayuso, J. G. (2001). Majority-logic-decodable cyclic arithmetic-modular AN-codes in 1, 2, and L steps. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2260, pp. 128–137). Springer Verlag. https://doi.org/10.1007/3-540-45325-3_12

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