Title :
On linear codes over a non-chain extension of F2 + uF2
Author :
Srinivasulu, B. ; Bhaintwal, Maheshanand
Author_Institution :
Dept. of Math., Indian Inst. of Technol. Roorkee, Roorkee, India
Abstract :
In this paper we study linear codes over a new ring R = F2 + uF2 + vF2 + uvF2 with u2 = 0, v2 = v and uv = vu, which is a non chain extension of the ring F2+uF2, u2 =0. We have obtained Mac Williams identities for Lee weight enumerator of linear codes over R using a Gray map from Rn to (F2 +uF2)n. We have studied self-dual codes over R and determined some existential conditions for Type I and Type II codes over R. Further we have briefly studied cyclic codes over R. It is shown that R[x]/〈xn - 1〉 is a PIR when n is odd. The form of the generator of a cyclic code of odd length over R is obtained.
Keywords :
Gray codes; cyclic codes; dual codes; linear codes; Gray map; Lee weight enumerator; MacWilliam identities; PIR; cyclic code; linear code; ring nonchain extension; self-dual codes; Electronic mail; Generators; Linear codes; Modules (abstract algebra); Polynomials;
Conference_Titel :
Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on
Conference_Location :
Hooghly
Print_ISBN :
978-1-4799-4446-0
DOI :
10.1109/C3IT.2015.7060155
