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On codes meeting the Griesmer bound

✍ Scribed by Andreas Klein

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
209 KB
Volume
274
Category
Article
ISSN
0012-365X

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Projective codes meeting the Griesmer bo
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✍ Tor Hellesth πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 399 KB

## 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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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.

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We give a characterization of codes meeting the Grey Rankin bound. When the codes have even length, the existence of such codes is equivalent to the existence of certain quasi-symmetric designs. We also find the parameters of all linear codes meeting the Grey Rankin bound. ## 1997 Academic Press T

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✍ Dmitrii Yu. Nogin πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 146 KB

We show that the minimum r-weight d P of an anticode can be expressed in terms of the maximum r-weight of the corresponding code. As examples, we consider anticodes from homogeneous hypersurfaces (quadrics and Hermitian varieties). In a number of cases, all di!erences (except for one) of the weight