25 citations · 117 across the 15 of their papers we have counts for
16 papers
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 Self-Dual Codes of length 68 from a 2 by 2 block matrix Construction and Group Rings
Maria Bortos, Joe Gildea, Abidin Kaya +2
Many generator matrices for constructing extremal binary self-dual codes of different lengths have the form G=(I|A), where I is the n by n identity matrix and A is the n by n matri…
Composite Matrices from Group Rings, Composite G-Codes and Constructions of Self-Dual Codes
Steven T. Dougherty, Joe Gildea, Adrian Korban +1
In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ri…
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…
New Self-Dual Codes from 2x2 Block Circulant Matrices, Group Rings and Neighbours of Neighbours
Joe Gildea, Abidin Kaya, Rhian Taylor +1
In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereb…
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…
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…
New extremal binary self-dual codes of lengths 64 and 66 from bicubic planar graphs
Abidin Kaya
In this work, connected cubic planar bipartite graphs and related binary self-dual codes are studied. Binary self-dual codes of length 16 are obtained by face-vertex incidence matr…
New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2
Abidin Kaya
In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frob…
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…
New extremal binary self-dual codes of lengths 66 and 68 from codes over r_k,m
Abidin Kaya, Nesibe Tüfekçi
In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings R_k,m. Self-dual binary codes are obtained as the Gray images…
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…
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…