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Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound

Announce Type: new Abstract: In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory...

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