The difference matrices of the classes of a Sharma-Kaushik partition

Bhu Dev Sharma; Norris Sookoo

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 1, page 23-31
  • ISSN: 0044-8753

Abstract

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Sharma-Kaushik partitions have been used to define distances between vectors with n -coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by the difference matrices of the classes of an SK-partition have another natural basis. The relationship between these two bases has been given.

How to cite

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Sharma, Bhu Dev, and Sookoo, Norris. "The difference matrices of the classes of a Sharma-Kaushik partition." Archivum Mathematicum 040.1 (2004): 23-31. <http://eudml.org/doc/249290>.

@article{Sharma2004,
abstract = {Sharma-Kaushik partitions have been used to define distances between vectors with $n$-coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by the difference matrices of the classes of an SK-partition have another natural basis. The relationship between these two bases has been given.},
author = {Sharma, Bhu Dev, Sookoo, Norris},
journal = {Archivum Mathematicum},
keywords = {SK-partitions; distance scheme; extended intersection number; distance scheme; extended intersection number; Bose-Mesner algebra; circulant matrices; difference matrices},
language = {eng},
number = {1},
pages = {23-31},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The difference matrices of the classes of a Sharma-Kaushik partition},
url = {http://eudml.org/doc/249290},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Sharma, Bhu Dev
AU - Sookoo, Norris
TI - The difference matrices of the classes of a Sharma-Kaushik partition
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 1
SP - 23
EP - 31
AB - Sharma-Kaushik partitions have been used to define distances between vectors with $n$-coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by the difference matrices of the classes of an SK-partition have another natural basis. The relationship between these two bases has been given.
LA - eng
KW - SK-partitions; distance scheme; extended intersection number; distance scheme; extended intersection number; Bose-Mesner algebra; circulant matrices; difference matrices
UR - http://eudml.org/doc/249290
ER -

References

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  9. Some tighter bounds on code size with Sharma-Kaushik metrics, Presented at the Intern. Conf. on Math., Mao, Menorca, June 15–17, 1987. 
  10. Error correcting codes through a new metric, 41st Annual Conf. Intern. Stat. Inst., New Delhi 1977. 
  11. Limites intensity random and burst error codes with class-weight considerations, Elektron. Inform.-verarb. Kybernetik 15 (1979), 315–321. MR0553671
  12. Algebra of Sharma and Kaushik’s metric inducing partitions of Z q , J. Combin. Inform. System Sci. 11 (1986), 19–32. MR0959671
  13. Association and other schemes related to Sharma-Kaushik class of distances over finite rings, Le Matematiche, Vol. XLV, Fasc. I (1990), 163–185. MR1181005
  14. Lectures Notes in Mathematics, Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Springer-Verlag, Berlin 1972. MR0392580

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