Results 31 to 40 of about 4,270,277 (317)
Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4)
Information, 2018 Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over
Sunghyu Han
doaj +1 more source
Classification of quaternary Hermitian self-dual codes of length 20 [PDF]
, 2010 A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.Comment: 9 pages.
Harada, Masaaki, Munemasa, Akihiro
core +1 more source
Complementary dual codes for counter-measures to side-channel attacks
Advances in Mathematics of Communications, 2016 We recall why linear codes with complementary duals (LCD codes) play a role in counter-measures to passive and active side-channel analyses on embedded cryptosystems. The rate and the minimum distance of such LCD codes must be as large as possible.
C. Carlet, S. Guilley
semanticscholar +1 more source
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
doaj +1 more source
New entanglement-assisted quantum codes constructed from Hermitian LCD codes
AIMS Mathematics, 2023 Hermitian linear complementary dual (LCD) codes are a class of linear codes that intersect with their Hermitian dual trivially. Each Hermitian LCD code can give an entanglement-assisted quantum error-correcting code (EAQECC) with maximal entanglement ...
Yuezhen Ren, Ruihu Li , Guanmin Guo
doaj +1 more source
Sultan Qaboos University Journal for Science, 2009 The group of characters of an elementary Abelian group has been used to define duality between its subgroups, which in turn is extended to duality between group codes.
Adnan Abdulla Zain
doaj +1 more source
Repeated-root constacyclic codes of length $ p_1p_2^t p^s $ and their dual codes
AIMS Mathematics, 2023 Let $ \mathbb{F}_q $ be the finite field with $ q = p^{k} $ elements, and $ p_{1}, p_{2} $ be two distinct prime numbers different from $ p $. In this paper, we first calculate all the $ q $-cyclotomic cosets modulo $ p_1p_2^t $ as a preparation for the ...
Hongfeng Wu, Li Zhu
doaj +1 more source
Catalytic quantum error correction [PDF]
, 2006 We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement.
Brun, Todd +2 more
core +2 more sources
Self-dual codes better than the Gilbert–Varshamov bound [PDF]
Des. Codes Cryptogr., 2017 We show that every self-orthogonal code over $${\mathbb {F}}_q$$Fq of length n can be extended to a self-dual code, if there exists self-dual codes of length n.
A. Bassa, H. Stichtenoth
semanticscholar +1 more source
The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring
AIMS Mathematics, 2023 In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd ...
Adel Alahmadi +2 more
doaj +1 more source