论文信息 - A note on the symmetry group of full rank perfect binary codes

A note on the symmetry group of full rank perfect binary codes

Abstract It is proved that the size of the symmetry group Sym ( C ) of every full rank perfect 1-error correcting binary code C of length n is less than or equal to 2 | Sym ( H n ) | / ( n + 1 ) , where H n is a Hamming code of the same length.

Olof Heden

[1] H. F. Mattson,et al. Perfect codes and the Mathieu groups , 1966 .

[2] Denis S. Krotov,et al. On the structure of non-full-rank perfect q-ary codes , 2009, Adv. Math. Commun..

[3] Sergey V. Avgustinovich,et al. On the Structure of Symmetry Groups of Vasil’ev Codes , 2005, Probl. Inf. Transm..

[4] Olof Heden,et al. On the size of the symmetry group of a perfect code , 2011, Discret. Math..

[5] Olof Heden,et al. On the symmetry group of extended perfect binary codes of length n+1 and rank n-log(n+1)+2 , 2012, Adv. Math. Commun..

[6] Kevin T. Phelps,et al. The Perfect Binary One-Error-Correcting Codes of Length 15: Part II—Properties , 2009, IEEE Transactions on Information Theory.

[7] Olof Heden,et al. On the existence of extended perfect binary codes with trivial symmetry group , 2009, Adv. Math. Commun..

[8] Kevin T. Phelps. Every finite group is the automorphism group of some perfect code , 1986, J. Comb. Theory, Ser. A.

[9] Alexander Vardy,et al. Perfect binary codes: constructions, properties, and enumeration , 1994, IEEE Trans. Inf. Theory.

[11] Olof Heden,et al. A survey of perfect codes , 2008, Adv. Math. Commun..

[12] A. Tietäväinen. On the Nonexistence of Perfect Codes over Finite Fields , 1973 .