Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes

This chapter is a survey of the recent results on the constructions of cyclicsubspace codes and maximum rank distance codes. Linearized polynomials are themain tools used to introduce both constructions in this chapter. In the constructionof cyclic subspace codes, codewords are considered as the root spaces of somesubspace polynomials (which are a particular type of linearized polynomials). Inthis set up, some algebraic manipulations on the coefficients and degrees of suchpolynomials are applied to provide a systematic construction of cyclic subspacecodes. In constructions of maximum rank distance codes, linearized polynomialsare used as codewords again, but in a different way. Codewords of rank metriccodes are considered as the linear maps that these polynomials represent. All knownconstructions of maximum rank distance codes in the literature are summarized usingthis linearized polynomial representation. Connections among the constructions andfurther explanations are also provided.


Construction of quasi-cyclic self-dual codes
Çomak, Pınar; Özbudak, Ferruh; Kim, Jon-Lark; Department of Cryptography (2013)
Quasi-cyclic and self-dual codes are interesting classes of linear codes. Quasi-cyclic codes are linear codes which takes maximum possible value of minimum distance among the codes with the same length and same dimension. Another class of interesting linear codes is the self-dual codes. Self-dual codes have close connections with group theory, lattice theory and design theory. There has been an active research on the classi fication of self-dual codes over fi nite fi elds and over rings. We study on constru...
Exhaustive study on the commutativity of time-varying systems
KÖKSAL, MUHAMMET (Informa UK Limited, 1988-5)
This paper, which is a survey and a compact reference on the commutativity of time-varying systems, gives the complete set of necessary and sufficient commutativity conditions for systems of any order. Original results are derived on Euler's systems, and explicit commutativity conditions are presented for fourth-order systems, which have not yet appeared in the literature.
Constructions and bounds on linear error-block codes
LİNG, San; Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-12-01)
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert-Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over F-2. We also study the asymptotic of linear error-block codes. We define the real valued function alpha (q,m,a) (delta), which is an analog of the important real valued function alpha (q) (delta) in the asymptotic theory of classical linear error-correctin...
Periodic solutions and stability of linear impulsive delay differential equations
ALZabut, Jehad; Ağacık, Zafer; Department of Mathematics (2004)
In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron co...
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields
Özbudak, Ferruh; YAYLA, OĞUZ (2014-09-18)
We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des ...
Citation Formats
F. Özbudak, Constructions of Cyclic Subspace Codes and Maximum Rank Distance Codes. 2018, p. 66.