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<p>In this paper, we introduce a construction method for a family of quasi-cyclic linear codes based on combinations of linear recurrence relations. Using this approach, we determine the weight distributions of a class of 2-quasi-cyclic codes. As an application, we provide two examples of strongly regular graphs whose corresponding codes are nonprojective. In addition, we show that some of the constructed codes are almost maximum distance separable (AMDS). In particular, one of the resulting graphs is the Paley graph.</p>

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Conditional recurrences and 2-quasi-cyclic codes

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Emre Güday,
  • Murat Sahin

摘要

In this paper, we introduce a construction method for a family of quasi-cyclic linear codes based on combinations of linear recurrence relations. Using this approach, we determine the weight distributions of a class of 2-quasi-cyclic codes. As an application, we provide two examples of strongly regular graphs whose corresponding codes are nonprojective. In addition, we show that some of the constructed codes are almost maximum distance separable (AMDS). In particular, one of the resulting graphs is the Paley graph.