Concatenated structure and a minimum distance bound for generalized quasi-cyclic codes

2017-06-10
Güneri, Cem
Özbudak, Ferruh
Özkaya, Buket
Saçıkara, Elif
Sepasdar, Zahra
Sole, Partick
Generalized quasi-cyclic (GQC) codes are mixed alphabet codes over a family of ring alphabets. Namely, if Rj := Fq[x]/hx mj − 1i for each j = 0, . . . , ` − 1 and positive integers m0, . . . , m`−1, an Fq[x]-submodule of R0 := R0 × · · · × R`−1 is called a GQC code. Compared to the special case of quasi-cyclic (QC) codes, allowing integers mj to be different gives freedom on the length of the code. We present a concatenated structure for GQC codes, which is more complicated to express than the QC case. Compatibility of the concatenated decomposition and the Chinese Remainder Theorem decomposition is also shown, which extends the analogous result of Güneri-Özbudak for QC codes. Concatenated structure also leads to a general minimum distance bound, extending the analogous bound for QC codes due to Jensen.
Citation Formats
C. Güneri, F. Özbudak, B. Özkaya, E. Saçıkara, Z. Sepasdar, and P. Sole, “Concatenated structure and a minimum distance bound for generalized quasi-cyclic codes,” presented at the The 13 th International Conference on Finite Fields and their Applications, June 4–10, 2017, Gaeta, Italy, 2017, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/87664.