منابع مشابه
Algebraic structures of MRD codes
Let Fq denote a finite field with q elements and let V = (Fq)m,n be the Fq-vector space of matrices over Fq of type (m,n). On V we define the so-called rank metric distance by d(A,B) = rank(A−B) for A,B ∈ V . Clearly, the distance d is a translation invariant metric on V . A subset C ⊆ V endowed with the metric d is called a rank metric code with minimum distance d(C) = min {d(A,B) | A 6= B ∈ V...
متن کاملOn self-dual MRD codes
We determine the automorphism group of Gabidulin codes of full length and characterise when these codes are equivalent to self-dual codes.
متن کاملOn dually almost MRD codes
In this paper we define and study a family of codes which come close to be MRD codes, so we call them AMRD codes (almost MRD). An AMRD code is a code with rank defect equal to 1. AMRD codes whose duals are AMRD are called dually AMRD. Dually AMRD codes are the closest to the MRD codes given that both they and their dual codes are almost optimal. Necessary and sufficient conditions for the codes...
متن کاملPD-sets for Z4-linear codes: Hadamard and Kerdock codes
Permutation decoding is a technique that strongly depends on the existence of a special subset, called PD-set, of the permutation automorphism group of a code. In this paper, a general criterion to obtain s-PD-sets of size s + 1, which enable correction up to s errors, for Z4-linear codes is provided. Furthermore, some explicit constructions of s-PD-sets of size s+1 for important families of (n...
متن کاملProofs of Data Possession and Retrievability Based on MRD Codes
Proofs of Data Possession (PoDP) scheme is essential to data outsourcing. It provides an efficient audit to convince a client that his/her file is available at the storage server, ready for retrieval when needed. An updated version of PoDP is Proofs of Retrievability (PoR), which proves the client’s file can be recovered by interactions with the storage server. We propose a PoDP/PoR scheme base...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2017
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2017.01.002