Results 31 to 40 of about 374,835 (257)
On Self-Dual Four Circulant Codes [PDF]
International Journal of Foundations of Computer Science, 2018 Four circulant codes form a special class of [Formula: see text]-generator, index [Formula: see text], quasi-cyclic codes. Under some conditions on their generator matrix 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.
Shi, Minjia +3 more
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Duality of codes over non-unital rings of order six
AIMS MathematicsSome basic theory on the duality of codes over two non-unital rings of order $ 6 $, namely $ H_{23} $ and $ H_{32} $ is presented. For a code $ {{\mathcal C}} $ over these rings, there is an associated binary code $ {{\mathcal C}}_a $ and a ternary code $
Altaf Alshuhail +2 more
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On skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $
AIMS Mathematics, 2023 The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code generated ...
Xuesong Si, Chuanze Niu
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Graph-Based Classification of Self-Dual Additive Codes over Finite Fields
, 2008 Quantum stabilizer states over GF(m) can be represented as self-dual additive codes over GF(m^2). These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence ...
Danielsen, Lars Eirik
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Group rings, G-codes and constructions of self-dual and formally self-dual codes [PDF]
Designs, Codes and Cryptography, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dougherty, Steven +3 more
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Additive Self-Dual Codes over GF(4) with Minimal Shadow
Information, 2018 We define additive self-dual codes over G F ( 4 ) with minimal shadow, and we prove ...
Sunghyu Han
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Extended binary Golay codes by a group algebra of one group
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2020 Extended binary Golay codes are examples of extreme binary self-dual codes of Type II (linear binary self-dual codes with Hamming distance between arbitrary codewords which are multiples of 4 that has the highest possible minimum Hamming distance among ...
М. Ю. Бортош +1 more
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New cubic self-dual codes of length 54, 60 and 66
, 2017 We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by constructing 1 new
Kim, Jon-Lark +2 more
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The build up construction for codes over a non-commutative non-unitary ring of order 9
AIMS MathematicsThe build-up method is a powerful class of propagation rules that generate self-dual codes over finite fields and unitary rings. Recently, it was extended to non-unitary rings of order four to generate quasi self-dual codes.
Adel Alahmadi +2 more
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New extremal binary self-dual codes of length 68 from quadratic residue codes over f_2+uf_2+u^2f_2
, 2013 In this work, quadratic reside codes over the ring F2 +uF2 +u^2F2 with u^3 = u are considered. A duality and distance preserving Gray map from F2 + uF2 + u^2F2 to (F_2)^3 is defined.
Kaya, Abidin +2 more
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