Abstract:It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field F and hyperinvariant subspaces of F n under an appropriate linear transformation.Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.

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Ab.~lracl-ln this paper we consider two models of roneatenated ronmlutionaJ rodes fr-om the perspeethoe of Unear systems theory. We present an Input-state-output representation of these models and we study the rondition

Steganography, as it is known, is a technique to hide a secret message within a message or collection of data that is not secret, and a problem in mathematics is to decipher the secret included in the message, to solve this problem a good tool It is the theory of codes. Unlike the existing works that use block codes to hide information using the steganographic process, in this work, we propose the use of convolutional coding theory in steganography to encrypt and decrypt messages methods to decrypt messages. Here, we suggest a steganographic protocol based on convolutional codes in which they are defined as discrete linear dynamical systems with which the properties on controllability and observability characteristic of linear systems theory can be applied, in particular the properties of output observability character which can be easily described using matrix language. The proposed decoding algorithm used for dissimulation is a linear decoding method, which has decreased both the time and space complexity, compared to the Viterbi decoding algorithm, sometimes used in other cases; indeed, we go from 2h.n to 2h=2.n, in memory space (with h: constraint height, and n: length of cover object). Moreover, the time complexity is better, while we can also denote that with the convolutional approach, we intend to take advantage of the time-depending transaction.