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Construction of MDS self-dual codes over Galois rings [PDF]
, 2017 The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction of self-dual codes over Galois rings as a GF(q)-analogue of (Kim and Lee, J Combin Theory ser A, 105:79-95).
이윤진
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The build-up construction of quasi self-dual codes over a non-unital ring
Journal of Algebra and its Applications, 2021 There is a local ring [Formula: see text] of order [Formula: see text] without identity for the multiplication, defined by generators and relations as [Formula: see text] We study a recursive construction of self-orthogonal codes over [Formula: see text]
Adel Alahmadi +5 more
semanticscholar +1 more source
Construction of extremal self-dual codes over Z8 and Z16 [PDF]
, 2017 We present a method of constructing free self-dual codes over Z8 and Z16 which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over Z2m can be found from a binary (extremal ...
이윤진
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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
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Z₂Z₄-additive formally self-dual codes [PDF]
, 2014 We study odd and even Z₂Z₄ formally self-dual codes. The images of these codes are binary codes whose weight enumerators are that of a formally self-dual code but may not be linear. Three constructions are given for formally self-dual codes and existence
Fernández Córdoba, Cristina +1 more
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Self-Dual Cyclic Codes Over M2(ℤ4)
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet.
Bhowmick Sanjit +3 more
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Advances in Mathematics of Communications, 2016 Improved exposition according to the referees ...
Gabriele Nebe, Wolfgang Willems
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Hermitian Self-Dual Abelian Codes [PDF]
IEEE Transactions on Information Theory, 2014 Hermitian self-dual abelian codes in a group ring Fq2[G], where Fq2 is a finite field of order q2 and G is a finite abelian group, are studied. Using the well-known discrete Fourier transform decomposition for a semisimple group ring, a characterization of Hermitian self-dual abelian codes in Fq2[G] is given, together with an alternative proof of ...
Somphong Jitman, San Ling, Patrick Solé
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Gottesman-Kitaev-Preskill codes: A lattice perspective [PDF]
Quantum, 2022 We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes.
Jonathan Conrad +2 more
doaj +1 more source
Rate adaptive binary erasure quantization with dual fountain codes [PDF]
, 2008 —In this contribution, duals of fountain codes are introduced and their use for lossy source compression is investigated. It is shown both theoretically and experimentally that the source coding dual of the binary erasure channel coding problem, binary ...
Mohamed Ismail +8 more
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