AN ALGORITHMIC APPROACH TO ACHIEVE MINIMUM $\\rho$-DISTANCE AT LEAST d IN LINEAR ARRAY CODES

• JAIN Sapna

  Department of Mathematics University of Delhi

Abstract

An array code/linear array code is a subset/subspace, respectively, of the linear space Mat_m×s(Fq), the space of all m × s matrices with entries froma finite field Fq endowed with a non-Hamming metric known as the RT-metric or $\\rho$-metric or m-metric. In this paper, we obtain a sufficient lower bound on the number of parity check digits required to achieve minimum $\\rho$-distance at least d in linear array codes using an algorithmic approach. The bound has been justified by an example. Using this bound, we also obtain a lower bound on the numberBq(m × s, d) where Bq(m × s, d) is the largest number of code matrices possiblein a linear array code V ⊆ Mat _{m × s} (Fq) having minimum $\\rho$-distance at least d.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 62 (1), 189-200, 2008

  Faculty of Mathematics, Kyushu University

Keywords

• linear array codes
• $\\rho$-distance
• $\\rho$-metric

Details

• CRID: 1390001205228098176
• NII Article ID: 110006648020
• NII Book ID: AA10994346
• DOI: 10.2206/kyushujm.62.189
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/62/1/62_1_189/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed