Korean J. Math. Vol. 25 No. 2 (2017) pp.201-209
DOI: https://doi.org/10.11568/kjm.2017.25.2.201

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

Main Article Content

Kwang Ho Kim
Young Ho Park

Abstract

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.


Article Details

References

[1] 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. Google Scholar

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

[3] Simeon Ball and Zsuasa Weiner, An Introduction to Finite Geometry (2011). Google Scholar

[4] Simeon Ball Finite Geometry and Combinatorial Applications, Cambridge University Press ( 2015). Google Scholar

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

[6] 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 . Google Scholar

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

[8] W. Cary Huffman and Vera Pless, Fundamentals of error correcting codes, Cambridge University Pless, New York, 2003. Google Scholar