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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, . doi:). 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.

New cubic self-dual codes of length 54, 60 and 66