Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Adrian Korban"'
Publikováno v:
IEEE Transactions on Information Theory. 69:1588-1603
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a4c6e0382b762a3f87c53a598264f15c
https://doi.org/10.1109/tit.2022.3217518
https://doi.org/10.1109/tit.2022.3217518
Publikováno v:
Advances in Mathematics of Communications. 17:994-1011
In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form \begin{document}$ [I_n \ | \ \Omega(v)], $\end{document} where \begin{document}$ I_n $\end{document
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51b2f83f8542472dabb1bf1870f0b3c0
https://doi.org/10.3934/amc.2021034
https://doi.org/10.3934/amc.2021034
Publikováno v:
Volume: 14, Issue: 1 191-200
Turkish Journal of Mathematics and Computer Science
Turkish Journal of Mathematics and Computer Science
Finding the minimum distance of linear codes is a non-deterministic polynomial-time-hard problem and different approaches are used in the literature to solve this problem. Although, some of the methods focus on finding the true distances by using exa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4de7a27b08ed11ac3a15b9c5ada54cc
https://doi.org/10.47000/tjmcs.982426
https://doi.org/10.47000/tjmcs.982426
Publikováno v:
Web of Science
In this paper, we give a matrix construction method for designing DNA codes that come from group matrix rings. We show that with our construction one can obtain reversible $G^k$-codes of length $kn,$ where $k, n \in \mathbb{N},$ over the finite commu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb00c0770ac1e538890376aaec941e24
https://doi.org/10.1007/s10623-022-01067-7
https://doi.org/10.1007/s10623-022-01067-7
Autor:
Adrian Korban
Publikováno v:
Journal of Algebra Combinatorics Discrete Structures and Applications. 8:91-105
In this paper, we extend the work done on $G$-codes over formal power series rings and finite chain rings $\mathbb{F}_q[t]/(t^i)$, to composite $G$-codes over the same alphabets. We define composite $G$-codes over the infinite ring $R_\infty$ as idea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::26d5c2e0bd3d32fb11ca180a75a07322
https://doi.org/10.13069/jacodesmath.935951
https://doi.org/10.13069/jacodesmath.935951
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 34:423-442
We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::800ae5582bdb728c1e0148c6bfa130b2
https://doi.org/10.1007/s00200-021-00515-6
https://doi.org/10.1007/s00200-021-00515-6
Publikováno v:
Cryptography and Communications. 13:601-616
In this work, we study a new family of rings, ${\mathscr{B}}_{j,k}$ B j , k , whose base field is the finite field ${\mathbb {F}}_{p^{r}}$ F p r . We study the structure of this family of rings and show that each member of the family is a commutative
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bafea8f3e21d4063f4e44ce61b7aa1a4
https://doi.org/10.1007/s12095-021-00487-x
https://doi.org/10.1007/s12095-021-00487-x
Publikováno v:
International Journal of Algebra and Computation. 31:471-490
In this work, we extend an established isomorphism between group rings and a subring of the [Formula: see text] matrices. This extension allows us to construct more complex matrices over the ring [Formula: see text] We present many interesting exampl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aa2389aaa17e7b0a05836c673d1cf469
https://doi.org/10.1142/s0218196721500223
https://doi.org/10.1142/s0218196721500223
Publikováno v:
Quantum Information Processing. 21
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e667948ba20efc9837e91ec035c15ac5
https://doi.org/10.1007/s11128-022-03500-1
https://doi.org/10.1007/s11128-022-03500-1
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 33:569-586
We define a self-dual code over a finite abelian group in terms of an arbitrary duality on the ambient space. We determine when additive self-dual codes exist over abelian groups for any duality and describe various constructions for these codes. We
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::224f94887e16951b89f8f8e48e7de41c
https://doi.org/10.1007/s00200-020-00473-5
https://doi.org/10.1007/s00200-020-00473-5