A Note on New Near-Extremal Type I Z4-Codes of Length 48
Matteo Mravić, Sanja Rukavina · Mathematics · 2025
The subject of this work is self-dual Type I Z4-codes of length 48. It is known that the usual upper bound for the minimum Euclidean weight for the self-dual Z4-codes cannot be achieved for this length and type of codes; i.e., extremal Type I Z4-codes of length 48 do not exist. We are therefore looking for near-extremal Type I Z4-codes of length 48. The only known Type I near-extremal Z4-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 Z4-codes of length 48. These codes are the first Type I near-extremal Z4-codes with a residue code of minimum weight 8.