2012, 6(4): 499-503. doi: 10.3934/amc.2012.6.499

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

1. 

Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India, India

Received  January 2012 Revised  June 2012 Published  November 2012

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.
Citation: Leetika Kathuria, Madhu Raka. Existence of cyclic self-orthogonal codes: A note on a result of Vera Pless. Advances in Mathematics of Communications, 2012, 6 (4) : 499-503. doi: 10.3934/amc.2012.6.499
References:
[1]

G. K. Bakshi and M. Raka, A class of constacyclic codes over a finite field,, Finite Fields Appl., 18 (2012), 362. 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., (). 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. 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. doi: 10.1007/s00200-008-0086-9.

[7]

V. Pless, Cyclotomy and cyclic codes, the unreasonable effectiveness of number theory,, in, 46 (1992), 91.

[8]

E. M. Rains and N. J. A. Sloane, Self-dual codes,, in, (1998), 177.

[9]

N. J. A. Sloane and J. G. Thompson, Cyclic self-dual codes,, IEEE Trans. Inform. Theory, 29 (1983), 364. doi: 10.1109/TIT.1983.1056682.

show all references

References:
[1]

G. K. Bakshi and M. Raka, A class of constacyclic codes over a finite field,, Finite Fields Appl., 18 (2012), 362. 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., (). 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. 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. doi: 10.1007/s00200-008-0086-9.

[7]

V. Pless, Cyclotomy and cyclic codes, the unreasonable effectiveness of number theory,, in, 46 (1992), 91.

[8]

E. M. Rains and N. J. A. Sloane, Self-dual codes,, in, (1998), 177.

[9]

N. J. A. Sloane and J. G. Thompson, Cyclic self-dual codes,, IEEE Trans. Inform. Theory, 29 (1983), 364. doi: 10.1109/TIT.1983.1056682.

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