Abstract
In this paper, we give a pseudo-random method to construct extremal Type II codes over ℤ4;. As an application, we give a number of new extremal Type II codes of lengths 24, 32 and 40, constructed from some extremal doubly-even self-dual binary codes. The extremal Type II codes of length 24 have the property that the supports of the codewords of Hamming weight 10 form 5-(24, 10, 36) designs. It is also shown that every extremal doubly-even self-dual binary code of length 32 can be considered as the residual code of an extremal Type II code over ℤ4.
| Original language | English |
|---|---|
| Pages (from-to) | 257-269 |
| Number of pages | 13 |
| Journal | Designs, Codes, and Cryptography |
| Volume | 16 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1999 Jan 1 |
| Externally published | Yes |
Keywords
- Extremal codes and type II codes
- Self-dual codes over ℤ
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics
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Cite this
Gaborit, P., & Harada, M. (1999). Construction of Extremal Type II Codes over ℤ4. Designs, Codes, and Cryptography, 16(3), 257-269. https://doi.org/10.1023/A:1008335912135