MacWilliams Identities of Linear Codes with Respect to RT Metric over Mn×s(F2[u,v]/<uk,v2,uv-vu>)

Minjia SHI; Jie TANG; Maorong GE

doi:10.1587/transfun.E100.A.2522

MacWilliams Identities of Linear Codes with Respect to RT Metric over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>)

Minjia SHI, Jie TANG, Maorong GE

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The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are obtained. Finally, we give two examples to illustrate the results we obtained.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.11 pp.2522-2527

Publication Date: 2017/11/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2522

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Minjia SHI
  Ministry of Education, Anhui University,Southeast University,School of Mathematical Sciences of Anhui University
Jie TANG
  School of Mathematical Sciences of Anhui University
Maorong GE
  School of Mathematical Sciences of Anhui University

Keyword

RT metric, weight enumerator, MacWilliams identities, dual code

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Minjia SHI, Jie TANG, Maorong GE, "MacWilliams Identities of Linear Codes with Respect to RT Metric over Mn×s(F2[u,v]/)" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 11, pp. 2522-2527, November 2017, doi: 10.1587/transfun.E100.A.2522.
Abstract: The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are obtained. Finally, we give two examples to illustrate the results we obtained.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2522/_p

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@ARTICLE{e100-a_11_2522,
author={Minjia SHI, Jie TANG, Maorong GE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={MacWilliams Identities of Linear Codes with Respect to RT Metric over Mn×s(F2[u,v]/)},
year={2017},
volume={E100-A},
number={11},
pages={2522-2527},
abstract={The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are obtained. Finally, we give two examples to illustrate the results we obtained.},
keywords={},
doi={10.1587/transfun.E100.A.2522},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - MacWilliams Identities of Linear Codes with Respect to RT Metric over Mn×s(F2[u,v]/)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2522
EP - 2527
AU - Minjia SHI
AU - Jie TANG
AU - Maorong GE
PY - 2017
DO - 10.1587/transfun.E100.A.2522
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2017
AB - The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over M_n×s(F₂[u,v]/<u^k,v²,uv-vu>) are obtained. Finally, we give two examples to illustrate the results we obtained.
ER -