Lee-extremal self-dual codes over 2 + u2 of lengths 23 and 24

Hyun Jin Kim

doi:10.1016/j.ffa.2014.03.002

Lee-extremal self-dual codes over ₂ + u₂ of lengths 23 and 24

Hyun Jin Kim

University College

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We completely classify the Lee-extremal self-dual codes over ₂+u₂ of lengths 23 and 24 with a nontrivial automorphism of odd order. In particular, we show that there is no Lee-extremal self-dual code of length 23 with a nontrivial automorphism of odd order, there are 41 inequivalent Lee-extremal Type I codes of length 24 with a nontrivial automorphism of odd order and there exists one Lee-extremal Type II code of length 24 with a nontrivial automorphism of odd order, up to equivalence. Moreover, Lee-extremal Type II codes of length 24 have an automorphism of order 3.

Original language	English
Pages (from-to)	18-33
Number of pages	16
Journal	Finite Fields and their Applications
Volume	29
DOIs	https://doi.org/10.1016/j.ffa.2014.03.002
Publication status	Published - 2014 Sept

Bibliographical note

Funding Information:
The author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) ( NRF-2013R1A1A2063240 ).

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
Engineering(all)
Applied Mathematics

Access to Document

10.1016/j.ffa.2014.03.002

Cite this

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title = "Lee-extremal self-dual codes over 2 + u2 of lengths 23 and 24",

abstract = "We completely classify the Lee-extremal self-dual codes over 2+u2 of lengths 23 and 24 with a nontrivial automorphism of odd order. In particular, we show that there is no Lee-extremal self-dual code of length 23 with a nontrivial automorphism of odd order, there are 41 inequivalent Lee-extremal Type I codes of length 24 with a nontrivial automorphism of odd order and there exists one Lee-extremal Type II code of length 24 with a nontrivial automorphism of odd order, up to equivalence. Moreover, Lee-extremal Type II codes of length 24 have an automorphism of order 3.",

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N2 - We completely classify the Lee-extremal self-dual codes over 2+u2 of lengths 23 and 24 with a nontrivial automorphism of odd order. In particular, we show that there is no Lee-extremal self-dual code of length 23 with a nontrivial automorphism of odd order, there are 41 inequivalent Lee-extremal Type I codes of length 24 with a nontrivial automorphism of odd order and there exists one Lee-extremal Type II code of length 24 with a nontrivial automorphism of odd order, up to equivalence. Moreover, Lee-extremal Type II codes of length 24 have an automorphism of order 3.

AB - We completely classify the Lee-extremal self-dual codes over 2+u2 of lengths 23 and 24 with a nontrivial automorphism of odd order. In particular, we show that there is no Lee-extremal self-dual code of length 23 with a nontrivial automorphism of odd order, there are 41 inequivalent Lee-extremal Type I codes of length 24 with a nontrivial automorphism of odd order and there exists one Lee-extremal Type II code of length 24 with a nontrivial automorphism of odd order, up to equivalence. Moreover, Lee-extremal Type II codes of length 24 have an automorphism of order 3.

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