29 research outputs found
New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2
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 Frobenius ring. We apply the constructions over
the ring F_2 + uF_2 and self-dual Type I [64, 32, 12]_2-codes with various
weight enumerators obtained as Gray images. By the use of an extension theorem
for self-dual codes we were able to construct 27 new extremal binary self-dual
codes of length 68. The existence of the extremal binary self-dual codes with
these weight enumerators was previously unknown.Comment: 10 pages, 5 table
Modified Quadratic Residue Constructions and New Exermal Binary Self-Dual Codes of Lengths 64, 66 and 68
In this work we consider modiļ¬ed versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary ļ¬eld and the rings F2 +uF2 and F4 +uF4 for diļ¬erent prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of diļ¬erent lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8]
New binary self-dual codes via a variation of the four-circulant construction
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 extremal binary self-dual codes of length 68.
More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed
New binary self-dual codes via a generalization of the four circulant construction
In this work, we generalize the four circulant construction for self-dual codes. By applying the constructions over the alphabets , , , we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed.https://www.mathos.unios.hr/mc/index.php/mc/article/view/352
Constructing Self-Dual Codes from Group Rings and Reverse Circulant Matrices
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Advances in Mathematics of Communications following peer review. The definitive publisher-authenticated version Gildea, J., Abidin, K., Adrian, K. & Bahattin, Y. (2020). Constructing Self-Dual Codes from Group Rings and Reverse Circulant Matrices. Advances in Mathematics of Communications. is available online at: https://www.aimsciences.org/article/doi/10.3934/amc.2020077?viewType=htmlIn this work, we describe a construction for self-dual codes in which we employ
group rings and reverse circulant matrices. By applying the construction directly over
different alphabets, and by employing the well known extension and neighbor methods
we were able to obtain extremal binary self-dual codes of different lengths of which
some have parameters that were not known in the literature before. In particular, we
constructed three new codes of length 64, twenty-two new codes of length 68, twelve
new codes of length 80 and four new codes of length 92