Linear complementary pair of group codes over finite principal ideal rings

12/24/2020

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by   Hualu Liu, et al.

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A pair (C, D) of group codes over group algebra R[G] is called a linear complementary pair (LCP) if C ⊕ D =R[G], where R is a finite principal ideal ring, and G is a finite group. We provide a necessary and sufficient condition for a pair (C, D) of group codes over group algebra R[G] to be LCP. Then we prove that if C and D are both group codes over R[G], then C and D^⊥ are permutation equivalent.