Explicit MDS Codes With Complementary Duals
نویسندگان
چکیده
منابع مشابه
Explicit MDS Codes with Complementary Duals
In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature. On the other hand, MDS codes form an optimal family of classical codes which have wide applications in...
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Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. MDS codes are optimal in the sense that the m...
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A linear code with a complementary dual (or an LCD code) is defined to be a linear code C whose dual code C⊥ satisfies C ∩ C⊥ = {0}. The algebraic characterization of LCD codes is given, and it is shown that asymptotically good LCD codes exist. LCD codes are shown to provide an optimum linear coding solution for the two-user binary adder channel. The nearest-neighbor (or maximum-likelihood) dec...
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In this paper we study codes $C_p(overline{{rm HiS}})$ where $p =3,7, 11$ defined by the 3- 7- and 11-modular representations of the simple sporadic group ${rm HS}$ of Higman and Sims of degree 100. With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes ha...
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MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in the code, the original information can be recovered. However, it was shown that in order to recover a single symbol erasure, only a fraction of 1/...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2018
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2018.2816934