New cubic self-dual codes of length 54, 60 and 66
Applicable Algebra in Engineering, Communication and Computing, 2018•Springer
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones.
We consider the binary quasi-cyclic codes of length 3 ℓ 3 ℓ with the algebraic approach of
Ling and Solé (IEEE Trans Inf Theory 47 (7): 2751–2760, 2001. doi: 10.1109/18.959257). In
particular, we improve the previous results by constructing 1 new binary 54, 27, 10, 6 new
60, 30, 12 and 50 new 66, 33, 12 cubic self-dual codes. We conjecture that there exist no
more binary cubic self-dual codes with length 54, 60 and 66.
We consider the binary quasi-cyclic codes of length 3 ℓ 3 ℓ with the algebraic approach of
Ling and Solé (IEEE Trans Inf Theory 47 (7): 2751–2760, 2001. doi: 10.1109/18.959257). In
particular, we improve the previous results by constructing 1 new binary 54, 27, 10, 6 new
60, 30, 12 and 50 new 66, 33, 12 cubic self-dual codes. We conjecture that there exist no
more binary cubic self-dual codes with length 54, 60 and 66.
Abstract
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length with the algebraic approach of Ling and Solé (IEEE Trans Inf Theory 47(7):2751–2760, 2001. doi: 10.1109/18.959257 ). In particular, we improve the previous results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50 new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more binary cubic self-dual codes with length 54, 60 and 66.
Springer