On self-dual negacirculant codes of index two and four
نویسندگان
چکیده
منابع مشابه
On self-dual negacirculant codes of index two and four
In this paper, we study a special kind of factorization of x + 1 over Fq, with q a prime power ≡ 3 (mod 4) when n = 2p, with p ≡ 3 (mod 4) and p is a prime. Given such a q infinitely many such p’s exist that admit q as a primitive root by the Artin conjecture in arithmetic progressions. This number theory conjecture is known to hold under GRH. We study the double (resp. four)-negacirculant code...
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Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes of odd dimension are shown to be consta-dihedral. Exact counting formulae are derived for DN codes. The special class of length a power of two is studied by means of Dickson polynomials, and is shown to contain families of codes with relative distances satisfying a modified Gilb...
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Four circulant codes form a special class of 2-generator, index 4, quasi-cyclic codes. Under some conditions on their generator matrices they can be shown to be self-dual. Artin primitive root conjecture shows the existence of an infinite subclass of these codes satisfying a modified Gilbert-Varshamov bound.
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A classical result of Conway and Pless is that a natural projection of the xed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual [13]. In this paper we prove that the same holds for involutions under some (quite strong) conditions on the codes. In order to prove it, we introduce a new family of binary codes: the semi self-dual codes. A binary self-orthogo...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2018
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-017-0455-0