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

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.