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In this paper, constructions of some double circulant self-dual codes bygeneralized cyclotomic classes of order two are presented. This technique isapplied to [72, 36, 12] binary highest know self-dual codes to obtain self-dualcodes over GF(2) and [32, 16, 8] almost optimal self-dual codes over GF(4).Based on the properties of generalized cyclotomy, some of these codes can beproved to possess good minimum weights.

Double Circulant Self-Dual Codes From Generalized Cyclotomic Classes of Order Two