A Note on New Near-Extremal Type I Z 4 -Codes of Length 48

Matteo Mravić and Sanja Rukavina ()
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Matteo Mravić: Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
Sanja Rukavina: Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia

Mathematics, 2025, vol. 13, issue 6, 1-10

Abstract: The subject of this work is self-dual Type I Z 4 -codes of length 48. It is known that the usual upper bound for the minimum Euclidean weight for the self-dual Z 4 -codes cannot be achieved for this length and type of codes; i.e., extremal Type I Z 4 -codes of length 48 do not exist. We are therefore looking for near-extremal Type I Z 4 -codes of length 48. The only known Type I near-extremal Z 4 -code of length 48 was constructed in 2015 by M. Harada. We adapted a known pseudo-random search method and found at least two new near-extremal Type I Z 4 -codes of length 48. These codes are the first Type I near-extremal Z 4 -codes with a residue code of minimum weight 8.

Keywords: Z 4 -code; Euclidean weight; self-dual code; Type I Z 4 -code; near-extremal Z 4 -code (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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