Geodesic
The difference matrices of the classes of a Sharma-Kaushik partition
Archivum mathematicum, Tome 40 (2004) no. 1, pp. 23-31 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 05B10, 05B20, 05E30, 94B99
Keywords: SK-partitions; distance scheme; extended intersection number 
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Sharma, Bhu Dev; Sookoo, Norris. The difference matrices of the classes of a Sharma-Kaushik partition. Archivum mathematicum, Tome 40 (2004) no. 1, pp. 23-31. http://geodesic.mathdoc.fr/item/ARM_2004_40_1_a2/

[1] Davis, P. J.: Circulant matrices. John Wiley and Sons, New York 1979. | MR | Zbl

[2] Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips J. Res. Rep. Suppl. 10 (1973). | MR | Zbl

[3] Kaushik, M. L.: Burst-error-correcting codes with weight contraints under a new metric. J. Cybern. 8 (1978), 183–202. | MR

[4] Kaushik, M. L.: Single error and burst error correcting codes through a new metric. J. Cybern. 9 (1979), 1–15. | MR | Zbl

[5] Kaushik, M. L.: Necessary and sufficient number of parity-checks correcting random errors and burst with weight constraints under a new metric. J. Cybern. 9 (1979), 81–90. | MR

[6] Kaushik, M. L.: Random error detecting and burst error correcting codes under a new metric. Indian J. Pure Appl. Math. 10 (1979), 1460–1468. | MR | Zbl

[7] Kaushik, M. L.: A new metric in the study of error correcting codes. Ph.D. Thesis, University of Delhi (1979).

[8] Kaushik, M. L.: Channels and bounds for class-metric codes. Rev. Roumaine Math. Pures Appl. 26 (1981), 1345–1350. | MR | Zbl

[9] Sharma, B. D.  and Dial, G.: Some tighter bounds on code size with Sharma-Kaushik metrics. Presented at the Intern. Conf. on Math., Mao, Menorca, June 15–17, 1987.

[10] Sharma, B. D. and Kaushik M. L.: Error correcting codes through a new metric. 41st Annual Conf. Intern. Stat. Inst., New Delhi 1977.

[11] Sharma, B. D. and Kaushik M. L.: Limites intensity random and burst error codes with class-weight considerations. Elektron. Inform.-verarb. Kybernetik 15 (1979), 315–321. | MR

[12] Sharma, B. D. and Kaushik M. L.: Algebra of Sharma and Kaushik’s metric inducing partitions of $Z_q$. J. Combin. Inform. System Sci. 11 (1986), 19–32. | MR

[13] Sharma, B. D. and Sookoo, N.: Association and other schemes related to Sharma-Kaushik class of distances over finite rings. Le Matematiche, Vol. XLV, Fasc. I (1990), 163–185. | MR

[14] Wallis, W. D., Street, A.  P.  and Wallis, J. S.: Lectures Notes in Mathematics, Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Springer-Verlag, Berlin 1972. | MR