Polynomial representation of additive cyclic codes and new quantum codes

01/02/2023

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by   Reza Dastbasteh, et al.

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We give a polynomial representation for additive cyclic codes over 𝔽_p^2. 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 𝔽_p. We classify all the symplectic self-dual, self-orthogonal, and nearly self-orthogonal additive cyclic codes over 𝔽_p^2. 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 𝔽_4.