# ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS

• SARI, MUSTAFA (Department of Mathematics Yildiz Technical University) ;
• SIAP, IRFAN (Department of Mathematics Yildiz Technical University) ;
• SIAP, VEDAT (Department of Mathematical Engineering Yildiz Technical University)
• Received : 2014.10.14
• Published : 2015.11.30

#### Abstract

This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].

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#### Cited by

1. A Note on One Weight and Two Weight Projective $\mathbb {Z}_{4}$ -Codes vol.63, pp.1, 2017, https://doi.org/10.1109/TIT.2016.2628408