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Two-weight codes from trace codes over $R_k$

Published 16 Dec 2016 in cs.IT and math.IT | (1612.05523v1)

Abstract: We construct a family of two-Lee-weight codes over the ring $R_k,$ which is defined as trace codes with algebraic structure of abelian codes. The Lee weight distribution of the two-weight codes is given. Taking the Gray map, we obtain optimal abelian binary two-weight codes by using the Griesmer bound. An application to secret sharing schemes is also given.

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