Structural properties and enumeration of 1-generator generalized quasi-cyclic codes

@article{Cao2011StructuralPA,
  title={Structural properties and enumeration of 1-generator generalized quasi-cyclic codes},
  author={Yonglin Cao},
  journal={Des. Codes Cryptography},
  year={2011},
  volume={60},
  pages={67-79}
}
Let Fq be a finite field of cardinality q,m1,m2, . . . ,ml be any positive integers, and Ai = Fq [x]/(xmi −1) for i = 1, . . . , l. A generalized quasi-cyclic (GQC) code of block length type (m1,m2, . . . ,ml) over Fq is defined as an Fq [x]-submodule of the Fq [x]-module A1× A2 ×· · ·× Al . By the Chinese Remainder Theorem for Fq [x] and enumeration results of submodules of modules over finite commutative chain rings, we investigate structural properties of GQC codes and enumeration of all 1… CONTINUE READING