Some results on cyclic codes over the ring R2,m

Reza SOBHANI; Maryam MOLAKARIMI

Article Details

Some results on cyclic codes over the ring R2,m

Authors:

Reza SOBHANI | Maryam MOLAKARIMI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1061-1074

Document Type:

Article

Publication Date:

5/2013

Document Language:

Turkish

Document ID (Org No.):

2000747498

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

Abstract:

 

Let Rk,m be  the ring F2m[u1,u2,...,uk]/\gen ui2, uiuj-ujui. In this paper, cyclic codes of arbitrary length n over the ring R2,m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F2m-basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one correspondence between cyclic codes of length 2n, n odd, over the ring Rk-1,m and cyclic codes of length n over the ring Rk,m. By determining the complete structure of cyclic codes of length 2 over R2,m, a mass formula for the number of these codes is given. Using this and the mentioned correspondence, the number of ideals of the rings R2,m and R3,m is determined. As a corollary, the number of cyclic codes of odd length n over the rings R2,m and R3,m is obtained.

 

Let Rk,m be  the ring F2m[u1,u2,...,uk]/\gen ui2, uiuj-ujui. In this paper, cyclic codes of arbitrary length n over the ring R2,m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F2m-basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one correspondence between cyclic codes of length 2n, n odd, over the ring Rk-1,m and cyclic codes of length n over the ring Rk,m. By determining the complete structure of cyclic codes of length 2 over R2,m, a mass formula for the number of these codes is given. Using this and the mentioned correspondence, the number of ideals of the rings R2,m and R3,m is determined. As a corollary, the number of cyclic codes of odd length n over the rings R2,m and R3,m is obtained.

Article Details

Some results on cyclic codes over the ring R2,m

Authors:

Reza SOBHANI | Maryam MOLAKARIMI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1061-1074

Document Type:

Article

Publication Date:

5/2013

Document Language:

Turkish

Document ID (Org No.):

2000747498

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Cyclic codes

codes over R2

m

Issues

Article Details

Some results on cyclic codes over the ring R2,m

Authors: Reza SOBHANI | Maryam MOLAKARIMI

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1061-1074

Document Type: Article

Publication Date: 5/2013

Document Language: Turkish

Document ID (Org No.): 2000747498

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Cyclic codes

codes over R2

m

Issues

Authors:

Reza SOBHANI | Maryam MOLAKARIMI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1061-1074

Document Type:

Article

Publication Date:

5/2013

Document Language:

Turkish

Document ID (Org No.):

2000747498

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098