نتایج جستجو برای: cyclic codes

تعداد نتایج: 173811  

2012
Jaskaran S. Bhullar

We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length...

Journal: :Finite Fields and Their Applications 2012

Journal: :Finite Fields and Their Applications 2014
Nian Li Chunlei Li Tor Helleseth Cunsheng Ding Xiaohu Tang

Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first family of cyclic codes has parameters [3m−1,3m−1−2m,4] and contains a class of conjectured cyclic codes and several new classes of optimal cyclic codes. The ...

Journal: :International Journal of Information and Coding Theory 2016

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

Journal: :Advances in Applied Mathematics 2000

Journal: :IEEE Transactions on Information Theory 2007

2013
Mingzhong Wu

We mainly investigate the structures of skew cyclic and skew quasicyclic codes of arbitrary length over Galois rings. Similar to [5], our results show that the skew cyclic codes are equivalent to either cyclic and quasi-cyclic codes over Galois rings. Moreover, we give a necessary and sufficient condition for skew cyclic codes over Galois rings to be free. A sufficient condition for 1-generator...

Journal: :Finite Fields and Their Applications 2023

Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear based on special polynomials over finite fields. The first family are extended primitive cyclic which affine-invariant. second reducible codes. parameters these their duals determined. As the ...

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