论文信息 - A Full Rank Perfect Code of Length 31

A Full Rank Perfect Code of Length 31

A full rank perfect 1-error correcting binary code of length 31 with a kernel of dimension 21 is described. This was the last open case of the rank-kernel problem of Etzion and Vardy.

Olof Heden

[1] Alexander Vardy,et al. On Perfect Codes and Tilings: Problems and Solutions , 1998, SIAM J. Discret. Math..

[2] Kevin T. Phelps,et al. On Perfect Codes: Rank and Kernel , 2002, Des. Codes Cryptogr..

[3] Alexander Vardy,et al. Resolving the Existence of Full-Rank Tilings of Binary Hamming Spaces , 2005, SIAM J. Discret. Math..

[4] Olof Heden. A remark on full rank perfect codes , 2006, Discret. Math..

[5] Sergey V. Avgustinovich,et al. On the Ranks and Kernels Problem for Perfect Codes , 2003, Probl. Inf. Transm..