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On the size of transducers for bidirectional decoding of prefix codes

Laura Giambruno, Sabrina Mantaci (2012)

RAIRO - Theoretical Informatics and Applications

In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this...

On the structure of linear recurrent error-control codes

Michel Fliess (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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.

On the structure of linear recurrent error-control codes

Michel Fliess (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

On the Weight Distribution of the Coset Leaders of Constacyclic Codes

Velikova, Evgeniya, Bojilov, Asen (2008)

Serdica Journal of Computing

Constacyclic codes with one and the same generator polynomial and distinct length are considered. We give a generalization of the previous result of the first author [4] for constacyclic codes. Suitable maps between vector spaces determined by the lengths of the codes are applied. It is proven that the weight distributions of the coset leaders don’t depend on the word length, but on generator polynomials only. In particular, we prove that every constacyclic code has the same weight distribution...

Optimal Locating-Total Dominating Sets in Strips of Height 3

Ville Junnila (2015)

Discussiones Mathematicae Graph Theory

A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, locating-total dominating sets in strips have been studied by Henning and Jafari Rad (2012). In particular,...

Parity codes

Paulo E. D. Pinto, Fábio Protti, Jayme L. Szwarcfiter (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Motivated by a problem posed by Hamming in 1980, we define even codes. They are Huffman type prefix codes with the additional property of being able to detect the occurrence of an odd number of 1-bit errors in the message. We characterize optimal even codes and describe a simple method for constructing the optimal codes. Further, we compare optimal even codes with Huffman codes for equal frequencies. We show that the maximum encoding in an optimal even code is at most two bits larger than the maximum...

Parity codes

Paulo E. D. Pinto, Fábio Protti, Jayme L. Szwarcfiter (2010)

RAIRO - Theoretical Informatics and Applications

Motivated by a problem posed by Hamming in 1980, we define even codes. They are Huffman type prefix codes with the additional property of being able to detect the occurrence of an odd number of 1-bit errors in the message. We characterize optimal even codes and describe a simple method for constructing the optimal codes. Further, we compare optimal even codes with Huffman codes for equal frequencies. We show that the maximum encoding in an optimal even code is at most two bits larger than the maximum...

Picture codes

Symeon Bozapalidis, Archontia Grammatikopoulou (2006)

RAIRO - Theoretical Informatics and Applications

We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set C of pictures a picture code B(C) which is the basis of the least DR-monoid including C. A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given.

Poids des duaux des codes BCH de distance prescrite 2 a + 1 et sommes exponentielles

Éric Férard (2002)

Bulletin de la Société Mathématique de France

Soit n un entier pair. On considère un code BCH binaire C n de longueur 2 n - 1 et de distance prescrite 2 a + 1 avec a ≥ 3 . Le poids d’un mot non nul du dual de  C n peut s’exprimer en fonction d’une somme exponentielle. Nous montrerons que cette somme n’atteint pas la borne de Weil et nous proposerons une amélioration de celle-ci. En conséquence, nous obtiendrons une amélioration de la borne de Carlitz-Uchiyama sur le poids des mots du dual de C n .

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