Emergent Mind

Classification and count of binary linear complementary dual group codes

(2201.08548)

Published Jan 21, 2022 in cs.IT , math.GR , math.IT , and math.RA

Abstract

We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and the minimum distance for LCD group codes are explored. Finally, we find a connection between LCD MDS group codes and maximal ideals.

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