MACWILLIAMS IDENTITIES FOR WEIGHT ENUMERATORS WITH RESPECT TO THE RT METRIC
Abstrak
Linear codes constitute an important family of error-correcting codes and have a rich algebraic structure. Initially, these codes were studied with respect to the Hamming metric; while for the past few years, they are also studied with respect to a non-Hamming metric, known as the Rosenbloom–Tsfasman metric (also known as RT metric or ρ metric). In this paper, we introduce and study the split ρ weight enumerator of a linear code in the R-module Mn×s(R) of all n × s matrices over R, where R is a finite Frobenius commutative ring with unity. We also define the Lee complete ρ weight enumerator of a linear code in Mn×s(ℤk), where ℤk is the ring of integers modulo k ≥ 2. We also derive the MacWilliams identities for each of these ρ weight enumerators.
Penulis (2)
AMIT K. SHARMA
ANURADHA SHARMA
Akses Cepat
- Tahun Terbit
- 2014
- Bahasa
- en
- Total Sitasi
- 5×
- Sumber Database
- CrossRef
- DOI
- 10.1142/s179383091450030x
- Akses
- Terbatas