منابع مشابه
On the genericity of maximum rank distance and Gabidulin codes
We consider linear rank-metric codes in Fqm . We show that the properties of being MRD (maximum rank distance) and non-Gabidulin are generic over the algebraic closure of the underlying field, which implies that over a large extension field a randomly chosen generator matrix generates an MRD and a non-Gabidulin code with high probability. Moreover, we give upper bounds on the respective probabi...
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In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable (MDS) codes. Using these properties, we show that, for MRD codes with error correction capability t, the deco...
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Reed-Solomon codes and Gabidulin codes have maximum Hamming distance and maximum rank distance, respectively. A general construction using skew polynomials, called skew Reed-Solomon codes, has already been introduced in the literature. In this work, we introduce a linearized version of such codes, called linearized Reed-Solomon codes. We prove that they have maximum sum-rank distance. Such dist...
متن کاملMaximum distance q -nary codes
t immaru-A q-nary error-correcting code with N = qk code words of length n = k + r can have no greater miniium distance d than r + 1. The class of codes for which d = r + 1 is studied first in general, then with the restriction that the codes be linear. Examples and construction methods are given to show that these codes exist for a number of values of q, k, and r. Proof: Pick any k position. T...
متن کاملSkew codes of prescribed distance or rank
In this paper we propose two methods to produce block codes of prescribed rank or distance. Following [4, 5] we work with skew polynomial rings of automorphism type and the codes we investigate are ideals in quotients of this ring. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section. 1 Galois theory of di...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2018
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-018-0833-3