Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Yıldız, Bahattin"'
Autor:
Mallik, Sudipta, Yildiz, Bahattin
Binary codes are constructed from incidence matrices of hypergraphs. A combinatroial description is given for the minimum distances of such codes via a combinatorial tool called ``eonv". This combinatorial approach provides a faster alternative metho
Externí odkaz:
http://arxiv.org/abs/2210.06733
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual
Externí odkaz:
http://arxiv.org/abs/2003.05296
In this work, we introduce the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the k-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight
Externí odkaz:
http://arxiv.org/abs/2002.10030
We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F_2 + uF_2 and F_4 + uF_4; using groups of order 3, 7, 9, 13, and 15. Through thes
Externí odkaz:
http://arxiv.org/abs/1912.11758
In this work, we generalize the four circulant construction for self-dual codes. By applying the constructions over the alphabets F_2, F_2 + uF_2, F_4+uF_4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extrem
Externí odkaz:
http://arxiv.org/abs/1912.11754
Autor:
Mallik, Sudipta, Yildiz, Bahattin
Binary linear codes are constructed from graphs, in particular, by the generator matrix $[I_n|A]$ where $A$ is the adjacency matrix of a graph on $n$ vertices. A combinatorial interpretation of the minimum distance of such codes is given. We also pre
Externí odkaz:
http://arxiv.org/abs/1908.03513
Autor:
Kaya, Abidin, Yildiz, Bahattin
In this work, we introduce new construction methods for self-dual codes using a Baumert-Hall array. We apply the constructions over the alphabets F_2 and F_4 + uF_4 and combine them with extension theorems and neighboring constructions. As a result,
Externí odkaz:
http://arxiv.org/abs/1902.01547
In this paper, we solve the reversibility problem for DNA codes over the non-chain ring $R_{k,s}=\mathbb{F}_{4^{2k}}[u_1,...,u_{s}]/< u_1^2-u_1,..., u_s^2-u_s>$. We define an automorphism $\theta$ over $R_{k,s}$ which help us both find the idempotent
Externí odkaz:
http://arxiv.org/abs/1711.02385
Given an $n\times n$ matrix $A$ over a field $F$ and a scalar $a\in F$, we consider the linear codes $C(A,a):=\{B\in F^{n\times n}\mid \,AB=aBA\}$ of length $n^2$. We call $C(A,a)$ a twisted centralizer code. We investigate properties of these codes
Externí odkaz:
http://arxiv.org/abs/1608.04079
Publikováno v:
Discrete Mathematics Vol 338 Issue 3 2016
In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of \lambda-circulant and \lambda-reverse circulant matrices. By using the constructions on $F_2$, we o
Externí odkaz:
http://arxiv.org/abs/1507.01628