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A characterization of codes meeting the Griesmer bound

✍ Scribed by Tor Helleseth


Book ID
114037550
Publisher
Elsevier Science
Year
1981
Weight
998 KB
Volume
50
Category
Article
ISSN
0019-9958

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On codes meeting the Griesmer bound
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We investigate codes meeting the Griesmer bound. The main theorem of this article is the generalization of the nonexistence theorem of Maruta (Des. Codes Cryptography 12 (1997) 83-87) to a larger class of codes.

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## Helleseth, T., Projective codes meeting the Griesmer bound, Discrete Mathematics 106/107 (1992) 265-271. We present a brief survey of projective codes meeting the Griesmer bound. Methods for constructing large families of codes as well as sporadic codes meeting the bound are given. Current res

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For any In, k, d; q]-code the Griesmer bound says that n >t ~ F d/q' 7. The purpose of this paper is to characterize all In, k, qk-1 \_ 3q~; q]-codes meeting the Griesmer bound in the case where k >/3, q >~ 5 and 1 ~</~ < k -1. It is shown that all such codes have a generator matrix whose columns co

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We prove that if a linear code over GF( p), p a prime, meets the Griesmer bound, then if p e divides the minimum weight, p e divides all word weights. We present some illustrative applications of this result.