Korean J. Math. Vol. 23 No. 1 (2015) pp.163-169
DOI: https://doi.org/10.11568/kjm.2015.23.1.163

Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$

Main Article Content

Young Ho Park


We give idempotent generators for quadratic residue codes over $p$-adic integers and over the rings $\mathbb{Z}_{p^e}$.

Article Details

Supporting Agencies

This study was supported by 2013 Research Grant from Kangwon National University (No. C1009751-01-01)


[1] A.R. Calderbank and N.J.A. Sloane, Modular and p-adic and cyclic codes, DCC, 6 (1995), 21–35. Google Scholar

[2] M.H Chiu, S. S.-T. Yau and Y. Yu, Z8-cyclic codes and quadratic residue codes, Advances in Algebra 25 (2000), 12–33. Google Scholar

[3] S.T. Dougherty, S.Y. Kim and Y.H. Park, Lifted codes and their weight enumer- ators, Discrite Math. 305 (2005), 123–135. Google Scholar

[4] S.T. Dougherty and Y.H. Park, Codes over the p-adic integers, Des. Codes. Cryptogr. 39 (2006), 65–80. Google Scholar

[5] W.C. Huffman and V. Pless, Fundamentals of error-correcting codes, Cambridge, 2003. Google Scholar

[6] S.J. Kim, Quadratic residue codes over Z16, Kangweon-Kyungki Math. J. 11 (2003), 57–64. Google Scholar

[7] S.J. Kim, Generator polynomials of the p-adic quadratic residue codes, Kangweon-Kyungki Math. J. 13 (2005), 103–112. Google Scholar

[8] F.J. MacWilliams and N.J.A. Sloane, The theory of error-correcting codes, North-Holland, Amsterdam, 1977. Google Scholar

[9] B.R. McDonald, Finite rings with identity, Dekker, New York, 1974. Google Scholar

[10] K. Nagata, F. Nemenzo and H. Wada, On self-dual codes over Z16, Lecture Notes in Computer Science 5527, 107–116, 2009. Google Scholar

[11] G. Nebe, E. Rains and N.J.A. Sloane, Self-dual codes and invariant theory, Springer-Verlag, 2006. Google Scholar

[12] Y.H. Park, Modular independence and generator matrices for codes over Zm, Des. Codes. Crypt 50 (2009), 147–162. Google Scholar

[13] B. Taeri, Quadratic residue codes over Z9, J. Korean Math Soc. 46 (2009), 13–30. Google Scholar