منابع مشابه
MDS codes in Doob graphs
Аннотация The Doob graph D(m, n), where m > 0, is the direct product of m copies of The Shrikhande graph and n copies of the complete graph K 4 on 4 vertices. The Doob graph D(m, n) is a distance-regular graph with the same parameters as the Hamming graph H(2m + n, 4). In this paper we consider MDS codes in Doob graphs with code distance d ≥ 3. We prove that if 2m + n > 6 and 2 < d < 2m + n, th...
متن کاملExtending MDS Codes
A q-ary (n,k)-MDS code, linear or not, satisfies n≤ q+ k−1. A code meeting this bound is said to have maximum length. Using purely combinatorial methods we show that an MDS code with n = q + k− 2 can be uniquely extended to a full length code if and only if q is even. This result is best possible in the sense that there is, for example, a non-extendable 4-ary (5,4)-MDS code. It may be that the ...
متن کاملAlmost MDS Codes
MDS codes are codes meeting the Singleton bound. Both for theory and practice, these codes are very important and have been studied extensively. Codes near this bound, but not attaining it, have had far less attention. In this paper we study codes that almost reach the Singleton bound.
متن کاملOn MDS elliptic codes
Munuera, C., On MDS elliptic codes, Discrete Mathematics 117 (1993) 2799286. In this paper we give a bound for MDS (maximum distance separable) algebraic-geometric codes arising from elliptic curves. Several consequences are presented.
متن کاملOn MDS Negacyclic LCD Codes
This paper is devoted to the study of linear codes with complementary-duals (LCD) arising from negacyclic codes over finite fields Fq, where q is an odd prime power. We obtain two classes of MDS negacyclic LCD codes of length n| q−1 2 , n| q+1 2 and a class of negacyclic LCD codes of length n = q+1. Also, we drive some parameters of Hermitian negacyclic LCD codes over Fq2 of length n = q − 1 an...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2011
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2010.2090246