منابع مشابه
New MDS or near MDS self-dual codes over finite fields
The study of MDS self-dual codes has attracted lots of attention in recent years. There are many papers on determining existence of q−ary MDS self-dual codes for various lengths. There are not existence of q−ary MDS self-dual codes of some lengths, even these lengths < q. We generalize MDS Euclidean self-dual codes to near MDS Euclidean self-dual codes and near MDS isodual codes. And we obtain ...
متن کاملNew MDS Self-Dual Codes over Large Finite Fields
We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes. ∗Faculty of Mathematics USTHB, University of Sciences and Technology of Algiers, B.P 32 El Alia, Bab Ezzouar, Algiers, Algeria
متن کاملOn Near-MDS Elliptic Codes
The Main Conjecture on maximum distance separable (MDS) codes states that, except for some special cases, the maximum length of a q-ary linear MDS code of is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near-MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near-MDS elliptic code ...
متن کاملMDS matrices over small fields: A proof of the GM-MDS conjecture
The GM-MDS conjecture of Dau et al. (ISIT 2014) speculates that the MDS condition, which guarantees the existence of MDS matrices with a prescribed set of zeros over large fields, is in fact sufficient for existence of such matrices over small fields. We prove this conjecture.
متن کاملUltimate Codes: Near-Optimal MDS Array Codes for RAID-6
As modern storage systems have grown in size and complexity, RAID-6 is poised to replace RAID-5 as the dominant form of RAID architectures due to its ability to protect against double disk failures. Many excellent erasure codes specially designed for RAID-6 have emerged in recent years. However, all of them have limitations. In this paper, we present a class of near perfect erasure codes for RA...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00168-5