Displaying similar documents to “Linear codes over finite chain rings.”

On the structure of linear recurrent error-control codes

Michel Fliess (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.

Construction of Optimal Linear Codes by Geometric Puncturing

Maruta, Tatsuya (2013)

Serdica Journal of Computing

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Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4. ∗This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138.

Divisible Codes - A Survey

Ward, Harold (2001)

Serdica Mathematical Journal

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This paper surveys parts of the study of divisibility properties of codes. The survey begins with the motivating background involving polynomials over finite fields. Then it presents recent results on bounds and applications to optimal codes.

On a complete set of operations for factorizing codes

Clelia De Felice (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set 𝒪 of operations exists such that each factorizing code can be obtained by using the operations in 𝒪 and starting with prefix or suffix codes. 𝒪 is named here a complete set of operations (for factorizing codes)....

Feedback equivalence of convolutional codes over finite rings

Noemí DeCastro-García (2017)

Open Mathematics

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The approach to convolutional codes from the linear systems point of view provides us with effective tools in order to construct convolutional codes with adequate properties that let us use them in many applications. In this work, we have generalized feedback equivalence between families of convolutional codes and linear systems over certain rings, and we show that every locally Brunovsky linear system may be considered as a representation of a code under feedback convolutional equivalence. ...

Ternary constant weight codes.

Östergård, Patric R.J., Svanström, Mattias (2002)

The Electronic Journal of Combinatorics [electronic only]

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On Multiple Deletion Codes

Landjev, Ivan, Haralambiev, Kristiyan (2007)

Serdica Journal of Computing

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In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion...