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<p>We describe the notion of independence and modular independence of vectors and count left and right linear codes over the non-commutative, non-unital, ring <i>E</i> of order 4. Moreover, we produce a Gray map which gives a bijection between right linear codes of length <i>n</i> and binary linear codes of length 2<i>n</i>.</p>

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Counting codes over a non-commutative rng of order 4

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Steven T. Dougherty,
  • Esengül Saltürk

摘要

We describe the notion of independence and modular independence of vectors and count left and right linear codes over the non-commutative, non-unital, ring E of order 4. Moreover, we produce a Gray map which gives a bijection between right linear codes of length n and binary linear codes of length 2n.