Results 1 to 10 of about 145 (141)

Skew Constacyclic Codes over a Non-Chain Ring [PDF]

Entropy, 2023
In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+1⟩ and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a
Mehmet Emin Köroğlu, Mustafa Sarı
doaj   +2 more sources

Low-Complexity Automorphism Ensemble Decoding of Reed-Muller Codes Using Path Pruning [PDF]

Entropy
The newly developed automorphism ensemble decoder (AED) leverages the rich automorphisms of Reed–Muller (RM) codes to achieve near maximum likelihood (ML) performance at short code lengths.
Kairui Tian, Rongke Liu, Zheng Lu
doaj   +2 more sources

On the Dimensions of Hermitian Subfield Subcodes from Higher-Degree Places [PDF]

Entropy
The focus of our research is the examination of Hermitian curves over finite fields, specifically concentrating on places of degree three and their role in constructing Hermitian codes.
Sabira El Khalfaoui, Gábor P. Nagy
doaj   +2 more sources

Quasi-Optimal Path Convergence-Aided Automorphism Ensemble Decoding of Reed–Muller Codes [PDF]

Entropy
By exploiting the rich automorphisms of Reed–Muller (RM) codes, the recently developed automorphism ensemble (AE) successive cancellation (SC) decoder achieves a near-maximum-likelihood (ML) performance for short block lengths.
Kairui Tian, He Sun, Yukai Liu, Rongke Liu   +3 more
doaj   +2 more sources

Automorphism Ensemble Decoding of Reed–Muller Codes [PDF]

IEEE Transactions on Communications, 2021
Accepted for Publication in IEEE Transactions on ...
Marvin Geiselhart, Ahmed Elkelesh, Moustafa Ebada, Sebastian Cammerer, Stephan ten Brink   +4 more
openaire   +2 more sources

The automorphisms and error orbits of Reed – Solomon codes

Доклады Белорусского государственного университета информатики и радиоэлектроники, 2020
The purpose of this work with its results presented in the article was to develop and transfer to the class of Reed – Solomon codes (RS-codes) the basic provisions of the theory of syndrome norms (TNS), previously developed for the noise-resistant coding
S. I. Semyonov, V. A. Lipnitsky
doaj   +1 more source

Syndrome spectrums of error orbits in RS-codes

Системный анализ и прикладная информатика, 2020
This article is devoted to the research of the properties of syndromes of errors in Reed-Solomon codes. RS-codes are built on non-binary alphabets. So, unlike BCH-codes, RS-codes contain an extremely large variety of correctable errors.
V. A. Lipnitski, S. I. Semyonov
doaj   +1 more source

Automorphism groups of cyclic codes [PDF]

Journal of Algebraic Combinatorics, 2009
In this article we study the automorphism groups of binary cyclic codes. In particular, we provide explicit constructions for codes whose automorphism groups can be described as (a) direct products of two symmetric groups or (b) iterated wreath products of several symmetric groups.
Bienert, Rolf, Klopsch, Benjamin
openaire   +2 more sources

Involutory permutation automorphisms of binary linear codes

Journal of Algebra and Its Applications, 2023
We investigate the properties of binary linear codes of even length whose permutation automorphism group is a cyclic group generated by an involution. Up to dimension or co-dimension [Formula: see text], we show that there is no quasi-group code whose permutation automorphism group is isomorphic to [Formula: see text].
Fatma Altunbulak Aksu, Roghayeh Hafezieh, İpek Tuvay   +2 more
openaire   +4 more sources

Error correction by Reed–Solomon codes using its automorphisms

Весці Нацыянальнай акадэміі навук Беларусі: Серыя фізіка-тэхнічных навук, 2021
The article explores the syndrome invariants of АГ-group of automorphisms of Reed–Solomon codes (RS-codes) that are a joint group of affine and cyclic permutations. The found real invariants are a set of norms of N Г-orbits that make up one or another АГ-
V. A. Lipnitsky, S. I. Semyonov
doaj   +1 more source