25 citations · 116 across the 17 of their papers we have counts for
19 papers
Codes from incidence matrices of hypergraphs
Sudipta Mallik, Bahattin Yildiz
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 ``…
New Extremal Binary Self-Dual Codes from Block Circulant Matrices and Block Quadratic Residue Circulant Matrices
Joe Gildea, Abidin Kaya, Rhian Taylor +2
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 wh…
New Extremal binary self-dual codes of length 68 from a novel approach to neighbors
Joe Gildea, Abidin Kaya, Adrian Korban +1
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 c…
A group induced four-circulant construction for self-dual codes and new extremal binary self-dual codes
Joe Gildea, Abidin Kaya, Alexander Tylyshchak +1
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 a…
New binary self-dual codes via a generalization of the four circulant construction
Joe Gildea, Abidin Kaya, Bahattin Yildiz
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…
Isodual and Self-dual Codes from Graphs
Sudipta Mallik, Bahattin Yildiz
Binary linear codes are constructed from graphs, in particular, by the generator matrix where is the adjacency matrix of a graph on vertices. A combinatorial inte…
New Extremal binary self-dual codes from a Baumert-Hall array
Abidin Kaya, Bahattin Yildiz
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 the…
Twisted Centralizer Codes
Adel Alahmadi, S. P. Glasby, Cheryl E. Praeger +2
Given an matrix over a field and a scalar , we consider the linear codes of length . We call …
New extremal binary self-dual codes from a modified four circulant construction
Abidin Kaya, Bahattin Yildiz, Abdullah Paşa
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 λ-circulant and λ-reverse cir…
The homogeneous weight for , related Gray map and new binary quasicyclic codes
Bahattin Yildiz, Ismail G. Kelebek
Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family , a recently introduced family of Frobenius…
The zero short Covering Problem for finite rings
Abdullah Paşa, Bahattin Yildiz
In this work, we find the cardinality of minimal zero short covers of An for any finite local ring A, removing the restriction of D(A)^2 = 0 from the previous works in the literatu…
On Codes Over with the Extended Lee Weight
Zeynep Ödemiş Özger, Bahattin Yildiz, Steven Dougherty
We consider codes over with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also con…
On codes over R_{k,m} and constructions for new binary self-dual codes
Nesibe Tufekci, Bahattin Yildiz
In this work, we study codes over the ring R_{k,m}=F_2[u,v]/<u^{k},v^{m},uv-vu>, which is a family of Frobenius, characteristic 2 extensions of the binary field. We introduce a dis…
New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic double circulant codes over F_4
Abidin Kaya, Bahattin Yildiz, Irfan Siap
In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes…
Extension theorems for self-dual codes over rings and new binary self-dual codes
Abidin Kaya, Bahattin Yildiz
In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F_2^…
New extremal binary self-dual codes of length 68 from quadratic residue codes over f_2+uf_2+u^2f_2
Abidin Kaya, Bahattin Yildiz, Irfan Siap
In this work, quadratic reside codes over the ring F2 +uF2 +u^2F2 with u^3 = u are considered. A duality and distance preserving Gray map from F2 + uF2 + u^2F2 to (F_2)^3 is define…
Linear Codes over Z_4+uZ_4: MacWilliams identities, projections, and formally self-dual codes
Bahattin Yildiz, Suat Karadeniz
Linear codes are considered over the ring Z_4+uZ_4, a non-chain extension of Z_4. Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, sy…
Quadratic Residue Codes over F_p+vF_p and their Gray Images
Abidin Kaya, Bahattin Yildiz, İrfan Siap
In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that…
The automorphism group of the doubly-even [72,36,16] code can only be of order 1, 3 or 5
Steven T Dougherty, Suat Karadeniz, Bahattin Yildiz
We prove that a putative code is not the image of linear code over $\ZZ_4$, $\FF_2 + u \FF_2$ or $\FF_2+v\FF_2$, thus proving that the extremal doubly even $[72,36,16]…