Title :
A Varshamov-Gilbert bound for a class of formally self-dual codes and related quantum codes
Author :
Tonchev, Vladimir D.
Author_Institution :
Dept. of Math. Sci., Michigan Technol. Univ., Houghton, MI, USA
fDate :
4/1/2002 12:00:00 AM
Abstract :
It is proved that a class of q-ary (2n,n) formally self-dual codes obtained from symmetric matrices over GF (q), contains codes that meet the Varshamov-Gilbert bound. The codes are self-dual with respect to the symplectic inner product and yield quantum codes encoding one state with n q-ary qubits and having minimum distance proportional to n
Keywords :
Galois fields; dual codes; linear codes; matrix algebra; quantum communication; Varshamov-Gilbert bound; formally self-dual codes; minimum distance; q-ary codes; quantum codes; qubits; symmetric matrices; symplectic inner product; Encoding; Galois fields; Hamming distance; Hamming weight; Linear code; Parity check codes; Rain; Space technology; Symmetric matrices;
Journal_Title :
Information Theory, IEEE Transactions on
