Some new non-additive maximum rank distance codes

Özbudak, Ferruh
In this paper, a construction of maximum rank distance (MRD) codes as a generalization of generalized Gabidulin codes is given. The family of the resulting codes is not covered properly by additive generalized twisted Gabidulin codes, and does not cover all twisted Gabidulin codes. When the basis field has more than two elements, this family includes also non-affine MRD codes, and such codes exist for all parameters. Therefore, these codes are the first non-additive MRD codes for most of the parameters.


A note on divisor class groups of degree zero of algebraic function fields over finite fields
Özbudak, Ferruh (Elsevier BV, 2003-01-01)
We give tight upper bounds on the number of degree one places of an algebraic function field over a finite field in terms of the exponent of a natural subgroup of the divisor class group of degree zero.. (C) 2002 Elsevier Science (USA). All rights reserved.
A relation between quasi-cyclic codes and 2-D cyclic codes
Guneri, Cem; Özbudak, Ferruh (Elsevier BV, 2012-01-01)
We consider a q-ary quasi-cyclic code C of length ml and index l, where both in and l are relatively prime to q. If the constituents of C are cyclic codes, we show that C can also be viewed as a 2-D cyclic code of size m x l over F(q). In case in and l are also coprime to each other, we easily observe that the code C must be equivalent to a cyclic code, which was proved earlier by Lim.
Fibre products of Kummer covers and curves with many points
Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-10-01)
We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (
Curves with many points and configurations of hyperplanes over finite fields
Özbudak, Ferruh (Elsevier BV, 1999-10-01)
We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
A minimum distance bound for quasi-nD-cyclic codes
Özbudak, Ferruh (Elsevier BV, 2016-09-01)
We provide a new concatenated structure for multidimensional quasi-cyclic (QnDC) codes over F-q and we give a trace representation for their codewords, which extends the known representations of QC and nD cyclic codes. Based on these results, we obtain a minimum distance bound for QnDC dyclic codes. Since QnDC codes are naturally related to nD convolutional codes, this bound also applies to a special class of 1-generator 2D convolutional codes.
Citation Formats
K. Otal and F. Özbudak, “Some new non-additive maximum rank distance codes,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 293–303, 2018, Accessed: 00, 2020. [Online]. Available: