A characterization of some {2υα+1+υγ+1, 2υα+υγ; k−1, 3}- minihypers and some (n,k, 3k−1 − 2 · 3α − 3γ; 3)-codes (k⩾3, 0⩽α<γ<k−1) meeting the Griesmer bound
نویسندگان
چکیده
منابع مشابه
Linear codes meeting the Griesmer bound, minihypers, and geometric applications
Coding theory and Galois geometries are two research areas which greatly influence each other. In this talk, we focus on the link between linear codes meeting the Griesmer bound and minihypers in finite projective spaces. Minihypers are particular (multiple) blocking sets. We present characterization results on minihypers, leading to equivalent characterization results on linear codes meeting t...
متن کاملCharacterization results on weighted minihypers and on linear codes meeting the Griesmer bound
We present characterization results on weighted minihypers. We prove the weighted version of the original results of Hamada, Helleseth, and Maekawa. Following from the equivalence between minihypers and linear codes meeting the Griesmer bound, these characterization results are equivalent to characterization results on linear codes meeting the Griesmer bound. 1. Linear codes meeting the Griesme...
متن کاملCharacterization results on arbitrary non-weighted minihypers and on linear codes meeting the Griesmer bound
We present characterization results on non-weighted minihypers. For minihypers in PG(k − 1, q), q not a square, we improve greatly the results of Hamada, Helleseth, and Maekawa, and of Ferret and Storme. The largest improvements are obtained for q prime.
متن کاملDivisibility of Codes Meeting the Griesmer Bound
The brackets of ``[n, k, d]'' signal that C is linear, and n is the length, k the dimension, and d the minimum weight of C. The bound was proved by Griesmer in 1960 for q=2 and generalized by Solomon and Stiffler in 1965. Over the years, much effort has gone into constructing codes meeting the bound or showing, for selected parameter values, that they do not exist. This effort is part of the mo...
متن کاملOn codes meeting the Griesmer bound
We investigate codes meeting the Griesmer bound. The main theorem of this article is the generalization of the nonexistence theorem of [7] to a larger class of codes. keywords: Griesmer bound, extending codes, nonexistence theorem, code construction
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90625-p