Polynomial representation of additive cyclic codes and new quantum codes

2023/01/02 by Dastbasteh, Reza, Shivji, Khalil · 1 citation
#Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2301.00753

Abstract

We give a polynomial representation for additive cyclic codes over \mathbbF_p². This representation will be applied to uniquely present each additive cyclic code by at most two generator polynomials. We determine the generator polynomials of all different additive cyclic codes. A minimum distance lower bound for additive cyclic codes will also be provided using linear cyclic codes over \mathbbF_p. We classify all the symplectic self-dual, self-orthogonal, and nearly self-orthogonal additive cyclic codes over \mathbbF_p². Finally, we present ten record-breaking binary quantum codes after applying a quantum construction to self-orthogonal and nearly self-orthogonal additive cyclic codes over \mathbbF₄.

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