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<p>Roth-Lempel (RL) codes were introduced by Roth and Lempel (IEEE Trans. Inf. Theory 35(3):655–657, 1989), which are a class of maximum distance separable (MDS) codes under certain condition and they are non generalized Reed-Solomon type. In this paper, we define generalized Roth-Lempel (GRL) codes over a finite field, which is a generalization of Roth-Lempel codes. We determine the parity-check matrix and characterize a necessary and sufficient condition that GRL codes are MDS and self-dual codes, respectively. As an application, we obtain covering radius and deep holes of GRL codes. Moreover, we present the quasi-cyclic structure of GRL codes.</p>

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New MDS and self-dual generalized Roth-Lempel codes as well as their deep holes

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Fengwei Li,
  • Ruiyuan Jiang,
  • Yuting Liu

摘要

Roth-Lempel (RL) codes were introduced by Roth and Lempel (IEEE Trans. Inf. Theory 35(3):655–657, 1989), which are a class of maximum distance separable (MDS) codes under certain condition and they are non generalized Reed-Solomon type. In this paper, we define generalized Roth-Lempel (GRL) codes over a finite field, which is a generalization of Roth-Lempel codes. We determine the parity-check matrix and characterize a necessary and sufficient condition that GRL codes are MDS and self-dual codes, respectively. As an application, we obtain covering radius and deep holes of GRL codes. Moreover, we present the quasi-cyclic structure of GRL codes.