A theory of two-dimensional cyclic codes
نویسندگان
چکیده
منابع مشابه
A Theory of Two-Dimensional Cyclic Codes
A basic theory of two-dimensional cyclic codes (TDC codes) is presented. This theory is applicable to the binary TDC codes of odd area, i.e., the TDC codes with an odd number of symbols from GF(2). It is shown that such TDC codes are completely characterized by the common zeros, which correspond to the roots for ordinary cyclic codes. The fundamental structure of the codes such as the positions...
متن کاملSome notes on the characterization of two dimensional skew cyclic codes
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...
متن کاملsome notes on the characterization of two dimensional skew cyclic codes
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...
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An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...
متن کاملA class of cyclic codes constructed via semiprimitive two-weight irreducible cyclic codes∗
We present a family of reducible cyclic codes constructed as a direct sum (as vector spaces) of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result of [10]. Moreover, despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute t...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1977
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(77)90232-7