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| Main Authors: | , |
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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2208.00324 |
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| _version_ | 1866911763290652672 |
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| author | Tang, Hopein Christofen Suprijanto, Djoko |
| author_facet | Tang, Hopein Christofen Suprijanto, Djoko |
| contents | We obtain all possible parameters of Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4,$ together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (\emph{Des Codes Cryptogr.} {\bf 88}(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4$ has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (\emph{Bull. Lond. Math. Soc.} {\bf 18}:97-122, 1986). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00324 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A general family of Plotkin-optimal two-weight codes over $\mathbb{Z}_4$ Tang, Hopein Christofen Suprijanto, Djoko Information Theory Combinatorics 94B 05, 05E 30 We obtain all possible parameters of Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4,$ together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (\emph{Des Codes Cryptogr.} {\bf 88}(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4$ has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (\emph{Bull. Lond. Math. Soc.} {\bf 18}:97-122, 1986). |
| title | A general family of Plotkin-optimal two-weight codes over $\mathbb{Z}_4$ |
| topic | Information Theory Combinatorics 94B 05, 05E 30 |
| url | https://arxiv.org/abs/2208.00324 |