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Punctured Binary Simplex Codes as LDPC codes
2022 61st FITCE International Congress Future Telecommunications: Infrastructure and Sustainability (FITCE), 2022 Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their performance and flexibility of operation, in wireless and mobile radio channels, as well as in cable transmission ...
Massimo Battaglioni +1 more
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New Quasi-Cyclic Codes From Simplex Codes [PDF]
IEEE Transactions on Information Theory, 2007 3 ...
Chen, Eric Zhi,
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On Best Erasure Wiretap Codes: Equivocation Matrices and Design Principles [PDF]
EntropyPhysical-layer security can aid in establishing secure telecommunication networks including cellular, Internet of Things, and telemetry networks, among others. Channel sounding techniques and/or telemetry systems for reporting channel conditions, coupled
Willie K. Harrison +3 more
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Perfect codes in the discrete simplex [PDF]
Designs, Codes, and Cryptography, 2013 We study the problem of existence of (nontrivial) perfect codes in the discrete $ n $-simplex $ Δ_{\ell}^n := \left\{ \begin{pmatrix} x_0, \ldots, x_n \end{pmatrix} : x_i \in \mathbb{Z}_{+}, \sum_i x_i = \ell \right\} $ under $ \ell_1 $ metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors ...
Mladen Kovačević +2 more
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Simplex Linear Codes Over the Ring F2 + vF2 [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعية, 2008 In this paper, we construct simplex linear codes over the ring of types , where and . We also determine some of their properties. These codes are extension and generalization of simplex codes over the rings .
Mohammed AL-Ashker, Ibtisam Isleem
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Partial permutation decoding for simplex codes
Advances in Mathematics of Communications, 2012 We show how to find $s$-PD-sets of size $s+1$ that satisfy the Gordon-Schonheim bound for partial permutation decoding for the binary simplex codes $\mathcal S_n(\mathbb F_2)$ for all $n \geq 4$, and for all values of $s$ up to $\left\lfloor\frac{2^n-1}{n}\right\rfloor -1$.
W Fish, Eric Mwambene
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Prior anogenital herpes and human papillomavirus infections are associated with increased risk of lichen sclerosus in a large retrospective cohort study [PDF]
International Journal of Women's DermatologyBackground:. Lichen sclerosus (LS) is an inflammatory mucocutaneous disorder typically affecting the anogenital region with unknown etiology. It is postulated that infectious etiologies could play a role in pathogenesis. Objective:.
Amit Singal, BA +2 more
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Hamming and simplex codes for the sum-rank metric
Designs, Codes, and Cryptography, 2020 Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $, base-field size $ q $ and field-extension degree $ m $ (i.e., number of matrix rows).
Umberto MartÍnez-Pen͂as
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Linear codes resulting from finite group actions [PDF]
Transactions on Combinatorics, 2022 In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same
Driss Harzalla
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Bounds on Covering Radius of Some Codes Over F₂ + uF₂ + vF₂ + uvF₂
IEEE Access, 2021 Let $R=\mathbb {F}_{2}+u\mathbb {F}_{2}+v\mathbb {F}_{2}+uv\mathbb {F}_{2}$ be a finite non-chain ring, where $u^{2}=u$ , $v^{2}=v$ , $uv=vu$ . We give the lower and upper bounds on the covering radius of different types of repetition codes for ...
Fanghui Ma, Jian Gao
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