On Codes Over R and its Bounds of Some kind of Block Repetition Codes in R

P Chella Pandian


This correspondence determines the lower and upper bounds of the covering radius in some kind of block repetition codes over the finite ring R=Z_2 Z_*, where Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. For covering radii of binary and octonary block repetition code over R is also discussed. This leads to the convenient formulation of code and arrives at the bounds.
Keywords: block repetition codes; covering radius; different weight; finite ring.

Korespondensi ini menentukan batas bawah dan batas atas dari jari-jari penutup suatu kode blok perulangan pada gelanggang hingga R=Z_2 Z_*, dengan Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. Dibahas juga jari-jari kode blok perulangan biner dan oktonari atas R. Diperoleh rumus untuk kode dan batasnya.
Kata Kunci: kode blok perulangan; penutup jari-jari; berat yang berbeda; gelanggang hingga.

2020MSC: 11T71, 94B05, 11H71.


block repetition codes; covering radius; different weight; finite ring.


P. Delsarte, "An algebraic approach to the association schemes of coding theory," Philips Research Rep. Suppl., vol. 10, 1973.

P. Delsarte and V. Levenshtein, "Association schemes and coding theory," IEEE Trans. Inform. Theory, vol. 44, no. 6, p. 2477–2504, 1998.

T. Abualrub, I. Siap and N. Aydin, "Z2Z4-additive cyclic codes," IEEE Trans. Inform. Theory, vol. 60, no. 3, p. 115–121, 2014.

M. Bilal, J. Borges, S. T. Dougherty and C. Fernandez-Cordoba, "Maximum distance separable codes over Z4 and Z2Z4," Des. Codes Cryptogr., vol. 61, no. 1, p. 31–40, 2011.

Borges, S. T. Dougherty and C. Fernandez-Cordoba, "Characterization and constructions of self-dual codes over Z2Z4," Adv. Math. Commun., vol. 6, no. 3, pp. 287-303, 2012.

Borges, C. Fernandez-Cordoba, J. Pujol, J. Rifa and M. Villanueva, "Z2Z4-linear codes: generator matrices and duality," Des. Codes Cryptogr., vol. 54, no. 2, p. 167–179, 2010.

P. P. Chella, "Bounds on the covering radius of some classes of codes over R," Open Journal of Discrete Applied Mathematics, vol. 2, no. 1, pp. 14-23, 2019.

P. P. Chella, "On codes over the finite non chain ring A = F4 + vF4, v2 = v and its covering radius of codes with Bachoc weight," International Journal of Algebra and Statistics, vol. 8, no. 1-2, pp. 12-18, 2019.

M. K. Raut and M. K. Gupta, "On octonary codes and their covering radii,".

C. Carlet, "Z2k -linear codes," IEEE Trans. Inform. Theory , vol. 44, no. 4, pp. 1543-1547, 1998.

I. Constantinescu, W. Heise and T. Honold, "Monomial extensions of isometries between codes over Zm,," in Proc. workshop ACCT’96, Sozopol, Bulgaria, 1996.

M. K. Gupta, D. G. Glynn and G. T. Aaron, "On senary simplex codes," in International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer, Berlin Heidelberg, 2001.

G. D. Cohen, M. G. Karpovsky, H. F. Mattson and J. R. Schatz, "Covering radius-survey and recent results," IEEE Trans. Inform. Theory, vol. 31, no. 3, p. 328–343, 1985.

Full Text: PDF

DOI: 10.15408/inprime.v4i2.27239


  • There are currently no refbacks.