Codes and Designs Related to Lifted MRD Codes
نویسندگان
چکیده
منابع مشابه
Some Optimal Codes From Designs
The binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. A new method is also introduced to study optimal codes.
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In this work we investigate unions of lifted MRD codes of a fixed dimension and minimum distance and derive an explicit formula for the cardinality of such codes. This will then imply a lower bound on the cardinality of constant dimension codes. We will first repeat some known results needed in this section. In Section 2 we will explain the construction and derive the formula for the cardinalit...
متن کاملsome optimal codes from designs
the binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. a new method is also introduced to study optimal codes.
متن کاملAlgebraic 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...
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We determine the automorphism group of Gabidulin codes of full length and characterise when these codes are equivalent to self-dual codes.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2013
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2012.2220119