2019/07/17 by Borello, Martino, de la Cruz, Javier, Willems, Wolfgang · 3 citations
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1907.07506
We give a short and elementary proof of the fact that for a linear complementary pair (C,D), where C and D are 2-sided ideals in a group algebra, D is uniquely determined by C and the dual code D^⊥ is permutation equivalent to C. This includes earlier results of Carlet et al. and Güneri et al. on nD cyclic codes which have been proved by subtle and lengthy calculations in the space of polynomials.