On p-Ary Local Frobenius Rings and their Homogeneous Weights

Authors

Bahattin Yildiz, Department of Mathematics, Fatih University, 34500 Buyukcekmece, Istanbul, TurkeyFollow
Makarim Abdlwahed Abdljabbar, Department of Mathematics, Fatih University, 34500 Buyukcekmece, Istanbul, Turkey\\ Computer College, University of Al Anbar, Al Anbar, IraqFollow

Author Country (or Countries)

Turkey

Abstract

In this work, a characterization of different properties of p-ary local Frobenius rings and their generating characters is given. Using the generating character, a general form for the homogeneous weights of such rings is described. In particular it is shown that the homogenous weights of all such rings have two non-zero values. Moreover, distance-preserving, linear Gray maps for the homogeneous weights of some classes of p-ary local Frobenius rings are found and using the Gray image, many linear p-ary codes attaining the Griesmer bound are counstructed.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100614

Recommended Citation

Yildiz, Bahattin and Abdlwahed Abdljabbar, Makarim (2016) "On p-Ary Local Frobenius Rings and their Homogeneous Weights," Applied Mathematics & Information Sciences: Vol. 10: Iss. 6, Article 14.
DOI: http://dx.doi.org/10.18576/amis/100614
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss6/14