Article Contents
Article Contents

# Existence of cyclic self-orthogonal codes: A note on a result of Vera Pless

• It is of interest to know when cyclic self-orthogonal codes of length $n$ over $\mathbb F_q$ do not exist. The conditions, listed by Pless in [7] under which cyclic self-orthogonal codes can not exist, are not always sufficient. An example is given to assert this. Here we give the necessary and sufficient conditions under which cyclic self-orthogonal codes of length $n$ over $\mathbb F_q$ do not exist.
Mathematics Subject Classification: Primary: 11T71; Secondary: 94B15.

 Citation:

•  [1] G. K. Bakshi and M. Raka, A class of constacyclic codes over a finite field, Finite Fields Appl., 18 (2012), 362-377.doi: 10.1016/j.ffa.2011.09.005. [2] G. K. Bakshi and M. Raka, Self-dual and self-orthogonal negacyclic codes of length $2p^n$ over a finite field, Finite Fields Appl., to appear. doi: 10.1016/j.ffa.2012.10.003. [3] D. M. Burton, "Elementry Number Theory,'' 6th edition, Tata McGraw-Hill, 2006. [4] W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge, 2003.doi: 10.1017/CBO9780511807077. [5] Y. Jia, S. Ling and C. Xing, On self-dual cyclic codes over finite fields, IEEE Trans. Inform. Theory, 57 (2011), 2243-2251.doi: 10.1109/TIT.2010.2092415. [6] X. S. Kai and S. X. Zhu, On cyclic self-dual codes, Appl. Algebra Engrg. Comm. Comput., 19 (2008), 509-525.doi: 10.1007/s00200-008-0086-9. [7] V. Pless, Cyclotomy and cyclic codes, the unreasonable effectiveness of number theory, in "Proc. Sympos. Appl. Math. (Orono, ME, 1991),'' Amer. Math. Soc., 46 (1992), 91-104. [8] E. M. Rains and N. J. A. Sloane, Self-dual codes, in "Handbook of Coding Theory'' (eds. V.S. Pless and W.C. Huffman), Elsevier, New York, (1998), 177-294. [9] N. J. A. Sloane and J. G. Thompson, Cyclic self-dual codes, IEEE Trans. Inform. Theory, 29 (1983), 364-367.doi: 10.1109/TIT.1983.1056682.