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

Author

Listed:
  • Matteo Mravić

    (Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
    These authors contributed equally to this work.)

  • Sanja Rukavina

    (Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Matteo Mravić & Sanja Rukavina, 2025. "A Note on New Near-Extremal Type I Z 4 -Codes of Length 48," Mathematics, MDPI, vol. 13(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:946-:d:1611169
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