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Minimal and optimal binary codes obtained using \(C_D\)-construction over the non-unital ring I

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Abstract

In this article, we construct linear codes over the commutative non-unital ring I of size four. We obtain their Lee-weight distributions and study their binary Gray images. Under certain mild conditions, these classes of binary codes are minimal and self-orthogonal. All codes in this article are few-weight codes. Besides, an infinite class of these binary codes consists of distance optimal codes with respect to the Griesmer bound.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, Delhi, 110016, India

    Vidya Sagar & Ritumoni Sarma

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  1. Vidya Sagar
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  2. Ritumoni Sarma
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VS and RS contributed equally to this work. Both authors read and approved the final manuscript.

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Correspondence to Ritumoni Sarma.

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Communicated by Y. Zhou.

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Sagar, V., Sarma, R. Minimal and optimal binary codes obtained using \(C_D\)-construction over the non-unital ring I. Des. Codes Cryptogr. 92, 145–157 (2024). https://doi.org/10.1007/s10623-023-01299-1

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