Indecomposability of cyclic codes

Indecomposability of cyclic codes

It is stated in Montpetit (1987) that cyclic codes are indecomposable, but it is not true in general. In fhis paper we will give a necessary and sufficient condition for a cyclic code to be indecomposable, using its generator polynomial. @ 1999 Elsevier Science B.V. All rights reserved

Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

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...

On quasi-cyclic codes as a generalization of cyclic codes

In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic codes of length lm and ideals of Ml(Fq)[X]/(X m −1). This permits to construct new classes of codes, namely quasi-BCH and quasi-evaluation codes. We study th...

Cyclic Codes

Polynomial Codes and Cyclic Codes

As an example, take F2, n = 5 and g(x) = x2 + x + 1. The code consists of the 8 codewords 0 · g(x), . . . , (x2 + x + 1) · g(x). Equivalently, we can identify every polynomial with its vector of coefficients to get a codeword in F2 . Verify that a polynomial code is linear and has dimension k = n −m. Also, check that if g(x) = ∑n−k i=0 gix i is the generator polynomial, then an n× k generating ...