A minimum distance bound for quasi-nD-cyclic codes

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.


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.
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.
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Codes on fibre products of some Kummer coverings
Özbudak, Ferruh (Elsevier BV, 1999-04-01)
The purpose of this paper is to construct fairly long geometric Goppa codes over F-q with rather good parameters by fibre products of some Kummer coverings, This paper also extends the results of Stepanov [1] and Stepanov and Ozbudak [2]. (C) 1999 Academic Press.
An identification theorem for groups of finite Morley rank and even type
Berkman, A; Borovik, AV (Elsevier BV, 2003-08-15)
The paper contains a construction of a definable BN-pair in a simple group of finite Morley rank and even type with a sufficiently good system of 2-local parabolic subgroups. This provides 'the final identification theorem' for simple groups of finite Morley rank and even type.
Citation Formats
F. Özbudak, “A minimum distance bound for quasi-nD-cyclic codes,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 193–222, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39645.