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Codes and designs from triangular graphs and their line graphs

Washiela Fish, Khumbo Kumwenda, Eric Mwambene (2011)

Open Mathematics

For any prime p, we consider p-ary linear codes obtained from the span over 𝔽 p p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.

On a test for codes.

Falucskai, J. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On the size of transducers for bidirectional decoding of prefix codes

Laura Giambruno, Sabrina Mantaci (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et 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 method is defined. It is proved also that this transducer...

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 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...

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...

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