More on the uniqueness of the Golay codes

✍ Scribed by Vera Pless

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 533 KB
• Volume: 106-107
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90569-2

✦ Synopsis

Pless, V., More on the uniqueness of the Golay codes, Discrete Mathematics 106/107 (1992) 391-398.

If c?' is a set of 3" ternary vectors of length 12, distance ~6, containing 0, then we show that the supports of the weight 6 vectors in C hold an S(5, 6, 12). Further we show that C must be a linear, self-dual [12,6,6] code, hence the Golay code. Also any set C of 36 ternary vectors of length 11, distance ~5, containing 0, is linear and hence the Golay [ll, 6,6,] code. The supports of the vectors of weight 5 in C hold an S(4, 5, 11).

Similarities and differences with the binary case are discussed.