Contents V.9, N.2, 2018

  • SKEW GENERALIZED QUASI-CYCLIC CODES
    TAHER ABUALRUB, MARTIANUS FREDERIC EZERMAN, PADMAPANI SENEVIRATNE, PATRICK SOL´E (pp. 123-134)
  • Abstract

    This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of both quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew generalized quasi-cyclic code C is a left submodule of R1×R2×. . .×Rℓ, where Ri , F[x; θ]/(xmi −1), with |⟨θ⟩| = m and m divides mi for all i ∈ {1, . . . , ℓ}. This description provides a direct construction of many codes with best-known parameters over GF(4). As a byproduct, some good asymmetric quantum codes detecting single bit-flip error can be derived from the constructed codes.

    Keywords

    generalized skew quasi-cyclic codes, skew polynomial codes, quasi-cyclic codes, quantum CSS codes.

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