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

Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communication and storage systems. However, their weight distributions are known only for a few cases mainly on the codes with one or two nonzeros. In this paper, the weight distributions of two classes of cyclic codes with three or four nonzeros are determ...

There are many results on the minimum distance of a cyclic code of the form that if a certain set T is a subset of the defining set of the code, then the minimum distance of the code is greater than some integer t. This includes the BCH, Hartmann-Tzeng, Roos, and shift bounds and generalizations of these (see below). In this paper we define certain projective varieties V (T, t) whose properties...

This paper present the construction cyclic isodual codes over finite fields and finite chain rings. These codes are monomially equivalent to their dual. Conditions are given for the existence of cyclic isodual codes. In addition, the concept of duadic codes over finite fields is extended to finite chain rings. Several constructions of isodual cyclic codes and self-dual codes are given.

We study ΘS−cyclic codes over the family of rings Ak. We characterize ΘS−cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is ΘS−cyclic then its Hermitian dual is also ΘS−cyclic. Finally, we give constructions of ΘS−cyclic codes. ∗Corresponding author. email: [email protected]

background: mesenchymal stem cells (mscs) can be expanded and differentiated into many mature cell types including smooth muscle cells (smcs). in addition to growth factor, cyclic stretch contributes to differentiation of stem cells. mechanical stimuli are critical to morphological changes, development, regeneration, differentiation and pathology of mesenchymal tissues. the aim of this study is...

A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese Remainder Theorem (CRT), or of the Discrete Fourier Transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower ...

A Z2Z4-additive code C ⊆ Z α 2 × Z β 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any simultaneous cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z4[x]-module Z2[x]/(x − 1)×Z4[x]/(x −1). Any Z2Z4-additive cyclic code C is of t...

A cyclic code is associated with another cyclic code to bound its minimum distance. The algebraic relation between these two codes allows the formulation of syndromes and a key equation. In this contribution, we outline the decoding approach for the case of errors and erasures and show how the Extended Euclidean Algorithm can be used for decoding.

In this paper we construct, using GAP System for Computational Discrete Algebra, some cyclic subspace codes, specially an optimal code over the finite field F210 . Further we present a definition and an example of the q-analogous of a m-quasi-cyclic subspace code over F28 .