论文信息 - New classes of self-complementary codes and quasi-symmetric designs

New classes of self-complementary codes and quasi-symmetric designs

We present a new technique for constructing binary error correcting codes and give some examples of codes that can be constructed via this method. Among the examples is an infinite family of self-complementary codes with parameters (2u2−u, 8u2, u2−u) that can be constructed whenever there exists a u × u Hadamard Matrix. These codes meet the Grey–Rankin bound and imply the existence of quasi-symmetric designs on 2u2−u points.

Carl Bracken

[1] Peter J. Cameron,et al. Near-regularity conditions for designs , 1973 .

[2] Gary McGuire,et al. Quasi-Symmetric Designs and Codes Meeting the Grey-Rankin Bound , 1997, J. Comb. Theory A.

[3] Carl Bracken,et al. New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices , 2006, Des. Codes Cryptogr..

[4] M. Shrikhande,et al. Quasi Symmetric Designs (London M , 1991 .

[5] M. Shrikhande,et al. Quasi-Symmetric Designs , 1991 .

[6] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .

[7] Ray Hill,et al. A First Course in Coding Theory , 1988 .