Squaring Construction for Repeated-Root Cyclic Codes
We considered repeated-root cyclic codes whose
block length is divisible by the characteristic of the underlying field.
Cyclic self dual codes are also the repeated root cyclic codes. It is
known about the one-level squaring construction for binary repeated
root cyclic codes. In this correspondence, we introduced of two
level squaring construction for binary repeated root cyclic codes of
length 2a b , a > 0, b is odd.
[1] E. Rains and N.J.A. Sloane, "Self-dual codes," in Handbook of Coding
Theory, V.S. Pless and W.C. Huffman (Editors), Elsevier, Amsterdam,
pp. 177-294, 1998.
[2] J. H. Conway and V. Pless, "On the enumeration of self-dual codes," J.
Combinatorial Theory, 28A, 26-53, 1980.
[3] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting
Codes, New York: North Holland, 1978.
[4] V. Pless and N. J. A. Sloane, "On the classi_cation and enumeration of
self-dual codes," J. Combinational Theory,18A 313-335, 1975.
[5] Carmen-Simona Nedeloaia, "Weight Distribution of Cyclic Self-Dual
Codes," IEEE Transactions on Information Theory, vol. 49, no.6 pp
1582-1591, June 2003.
[6] N. J. A. Sloane and J. G. Thompson, "Cyclic self-dual codes," IEEE
Trans. Inform. Theory, vol. IT-29, no. 3, pp. 364-366, May 1983.
[7] J. H. van Lint, "Repeated-root cyclic codes," IEEE Trans. Inform.
Theory, vol. 37, no. 2, pp. 343-345, Mar. 1991.
[8] G. Castagnoli, J. L. Massey, Ph. A. Shoeller, and N. von Seemann, "On
repeated-root cyclic codes," IEEE Trans. Inform. Theory, vol. 37, no.
2, pp. 337-342, Mar. 1991.
[9] W.Cary Huffman and Vera Pless, Fundamentals of Error-Corrrecting
Codes, Cambridge university press, 2003.
[10] V. Pless, Introduction to the Theory of Error Correcting Codes, 3rd ed.
New York: Wiley, 1998.
[11] Bas Heijne, "Cyclic Self-Dual Codes", Master's Thesis
Rijksuniversiteit Groningen, 7 MAY 2007,
http://scripties.fwn.eldoc.ub.rug.nl/FILES/scripties/Wiskunde/Masters
/2007/Heijne.B./Bas Heijne doctoraal WM 2007.pdf
[12] E.J.H. Brandenburg , "Finding the Minimal Distance of Cyclic
Self-Dual Codes", Bachelor-s Thesis Rijksuniversiteit Groningen,
March 2009,
[1] E. Rains and N.J.A. Sloane, "Self-dual codes," in Handbook of Coding
Theory, V.S. Pless and W.C. Huffman (Editors), Elsevier, Amsterdam,
pp. 177-294, 1998.
[2] J. H. Conway and V. Pless, "On the enumeration of self-dual codes," J.
Combinatorial Theory, 28A, 26-53, 1980.
[3] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting
Codes, New York: North Holland, 1978.
[4] V. Pless and N. J. A. Sloane, "On the classi_cation and enumeration of
self-dual codes," J. Combinational Theory,18A 313-335, 1975.
[5] Carmen-Simona Nedeloaia, "Weight Distribution of Cyclic Self-Dual
Codes," IEEE Transactions on Information Theory, vol. 49, no.6 pp
1582-1591, June 2003.
[6] N. J. A. Sloane and J. G. Thompson, "Cyclic self-dual codes," IEEE
Trans. Inform. Theory, vol. IT-29, no. 3, pp. 364-366, May 1983.
[7] J. H. van Lint, "Repeated-root cyclic codes," IEEE Trans. Inform.
Theory, vol. 37, no. 2, pp. 343-345, Mar. 1991.
[8] G. Castagnoli, J. L. Massey, Ph. A. Shoeller, and N. von Seemann, "On
repeated-root cyclic codes," IEEE Trans. Inform. Theory, vol. 37, no.
2, pp. 337-342, Mar. 1991.
[9] W.Cary Huffman and Vera Pless, Fundamentals of Error-Corrrecting
Codes, Cambridge university press, 2003.
[10] V. Pless, Introduction to the Theory of Error Correcting Codes, 3rd ed.
New York: Wiley, 1998.
[11] Bas Heijne, "Cyclic Self-Dual Codes", Master's Thesis
Rijksuniversiteit Groningen, 7 MAY 2007,
http://scripties.fwn.eldoc.ub.rug.nl/FILES/scripties/Wiskunde/Masters
/2007/Heijne.B./Bas Heijne doctoraal WM 2007.pdf
[12] E.J.H. Brandenburg , "Finding the Minimal Distance of Cyclic
Self-Dual Codes", Bachelor-s Thesis Rijksuniversiteit Groningen,
March 2009,
@article{"International Journal of Information, Control and Computer Sciences:60318", author = "O. P. Vinocha and J. S. Bhullar and Manish Gupta", title = "Squaring Construction for Repeated-Root Cyclic Codes", abstract = "We considered repeated-root cyclic codes whose
block length is divisible by the characteristic of the underlying field.
Cyclic self dual codes are also the repeated root cyclic codes. It is
known about the one-level squaring construction for binary repeated
root cyclic codes. In this correspondence, we introduced of two
level squaring construction for binary repeated root cyclic codes of
length 2a b , a > 0, b is odd.", keywords = "Squaring Construction, generator matrix, selfdual codes, cyclic codes, coset codes, repeated root cycliccodes.", volume = "4", number = "5", pages = "977-3", }
