82 research outputs found

    Construction of Some Optimal Ternary Linear Codes and the Uniqueness of [294, 6, 195; 3]-Codes Meeting the Griesmer Bound

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    AbstractLet nq(k, d) denote the smallest value of n for which there exists an [n, k, d; q]-code. It is known (cf. (J. Combin. Inform. Syst. Sci.18, 1993, 161–191)) that (1) n3(6, 195) ∈ {294, 295}, n3(6, 194) ∈ {293, 294}, n3(6, 193) ∈ {292, 293}, n3(6, 192) ∈ {290, 291}, n3(6, 191) ∈ {289, 290}, n3(6, 165) ∈ {250, 251} and (2) there is a one-to-one correspondence between the set of all nonequivalent [294, 6, 195; 3]-codes meeting the Griesmer bound and the set of all {v2 + 2v3 + v4, v1 + 2v2 + v3; 5, 3}-minihypers, where vi = (3i − 1)/(3 − 1) for any integer i ≥ 0. The purpose of this paper is to show that (1) n3(6, 195) = 294, n3(6, 194) = 293, n3(6, 193) = 292, n3(6, 192) = 290, n3(6, 191) = 289, n3(6, 165) = 250 and (2) a [294, 6, 195; 3]-code is unique up to equivalence using a characterization of the corresponding {v2 + 2v3 + v4, v1 + 2v2 + v3; 5, 3}-minihypers

    A construction of bent functions from plateaued functions

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    In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analysed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent function with some additional properties that enable the construction of strongly regular graphs are constructed, and explicit expressions for bent functions with maximal degree are presented

    A New Three-Valued Cross Correlation Betweenmm-Sequences of Different Lengths

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