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In this work we consider all the 11616 cyclic Steiner triple systems of order 45 (STS(45)) and establish that 600 of them are cyclically resolvable yielding 2128 point-cyclic Kirkman triple systems of order 45 (KTS(45)). We also find out that 106 of the 600 cyclically resolvable STS(45) are anti-Pasch, and are therefore of particular interest for the construction of optimal erasure-resilient codes.

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Point-Cyclic KTS(45)

  • 会议论文

  • 发表日期：

    2025年

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  • Svetlana Topalova,
  • Stela Zhelezova

摘要

In this work we consider all the 11616 cyclic Steiner triple systems of order 45 (STS(45)) and establish that 600 of them are cyclically resolvable yielding 2128 point-cyclic Kirkman triple systems of order 45 (KTS(45)). We also find out that 106 of the 600 cyclically resolvable STS(45) are anti-Pasch, and are therefore of particular interest for the construction of optimal erasure-resilient codes.