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<p>The idea of cyclic burst distance and weight was first proposed by Bridwell and Wolf (1970) to address multiple cyclic bursts. In this regard, Villalba et al. (2014) investigated the generalised Reiger bound for linear codes equipped with cyclic burst distance. In this paper, we propose an improvement in the bound. In addition, we also present some well-known bounds like the Plotkin bound, volume bound, mixed upper bound for codes which are equipped with cyclic burst distance. To do this, we first count the number of multiple bursts in an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation>-tuple having cyclic burst weight <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(t\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>t</mi> </math></EquationSource> </InlineEquation> or less. Lastly, we investigate these bounds regarding their superiority over one another, including the already existing ones.</p>

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Bounds on size of codes equipped with cyclic burst–b distance

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Pankaj Kumar Das,
  • Achal Agarwal

摘要

The idea of cyclic burst distance and weight was first proposed by Bridwell and Wolf (1970) to address multiple cyclic bursts. In this regard, Villalba et al. (2014) investigated the generalised Reiger bound for linear codes equipped with cyclic burst distance. In this paper, we propose an improvement in the bound. In addition, we also present some well-known bounds like the Plotkin bound, volume bound, mixed upper bound for codes which are equipped with cyclic burst distance. To do this, we first count the number of multiple bursts in an \(n\) n -tuple having cyclic burst weight \(t\) t or less. Lastly, we investigate these bounds regarding their superiority over one another, including the already existing ones.