On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
Generalized quasi-cyclic codes: structural properties and code construction
Applicable Algebra in Engineering, Communication and Computing
Low complexity encoder for generalized quasi-cyclic codes coming from finite geometries
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
A link between quasi-cyclic codes and convolutional codes
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes .I. Finite fields
IEEE Transactions on Information Theory
Cyclic and negacyclic codes over finite chain rings
IEEE Transactions on Information Theory
A class of 1-generator quasi-cyclic codes
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes III: generator theory
IEEE Transactions on Information Theory
Constructing quasi-cyclic codes from linear algebra theory
Designs, Codes and Cryptography
Trace representation of quasi-negacyclic codes
BICS'13 Proceedings of the 6th international conference on Advances in Brain Inspired Cognitive Systems
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Let F q be a finite field of cardinality q, m 1, m 2, . . . , m l be any positive integers, and $${A_i=F_q[x]/(x^{m_i}-1)}$$ for i = 1, . . . , l. A generalized quasi-cyclic (GQC) code of block length type (m 1, m 2, . . . , m l ) over F q is defined as an F q [x]-submodule of the F q [x]-module $${A_1\times A_2\times\cdots\times A_l}$$ . By the Chinese Remainder Theorem for F q [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-generator GQC codes and 1-generator GQC codes with a fixed parity-check polynomial respectively. Furthermore, we give an algorithm to count numbers of 1-generator GQC codes.