The mass formula of self-orthogonal codes over $\mathbf {GF(q)}$

Kwang Ho Kim, Young Ho Park


There exists already mass formula which is the number of self orthogonal codes in $GF(q)^n$, but not  proof of it. In this paper we described some theories about finite geometry and by using them proved the mass formula when $q=p^m$, $p$ is odd prime.


mass formula, self-orthogonal codes.

Full Text:



V.S. Pless, The number of isotropic subspace in a finite geometry, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 39 (1965), 418–421.

V.S. Pless, On the uniqueness of the Golay codes, J. Combin. Theory 5 (1968), 215–228.

Simeon Ball and Zsuasa Weiner, An Introduction to Finite Geometry (2011).

Simeon Ball Finite Geometry and Combinatorial Applications, Cambridge University Press ( 2015).

R.A.L. Betty and A. Munemasa, Mass formula for self-orthogonal codes over Zp2 , J.Combin.Inform.System sci.,

J.M.P. Balmaceda, R.A.L. Betty and F.R. Nemenzo, Mass formula for self-dual codes over Zp2 , Discrete Math. 308 (2008), 2984–3002 .

Y.H. Park, The classification of self-dual modular codes, Finite Fields and Their Applications 17 (5) (2011), 442–460.

W. Cary Huffman and Vera Pless, Fundamentals of error correcting codes, Cambridge University Pless, New York, 2003.



  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: