Quadratic Residue Codes over Z 9
نویسندگان
چکیده
A subset of n tuples of elements of Z9 is said to be a code over Z9 if it is a Z9-module. In this paper we consider an special family of cyclic codes over Z9, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over finite fields.
منابع مشابه
Self-dual codes and quadratic residue codes over the ring $\mathbb{Z}_9+u\mathbb{Z}_9$
In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over Z9+uZ9 with u 2 = u. Some results on self-dual codes over this ring are investigated. Further, the structural properties of quadratic residue codes are also considered. Two self-dual codes with parameters [22, 11, 5] and [24, 12, 9] over Z9 are obtained.
متن کاملType II codes over Z4
Type II Z 4-codes are introduced as self-dual codes over the integers modulo 4 containing the all-one vector and with euclidean weights multiple of 8: Their weight enumerators are characterized by means of invariant theory. A notion of extremality for the euclidean weight is introduced. Their binary images under the Gray map are formally self-dual with even weights. Extended quadratic residue Z...
متن کاملQuadratic residue codes over a non - chain ring extension of F 2
The focus in this work is on quadratic residue codes over the ring F2+vF2. We define these codes in terms of their idempotent generators and show that these codes share the properties analogous to that of quadratic residue codes over finite fields. We study Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes over F2 + vF2. Further, we obtain two optimal self-...
متن کاملQuadratic Residue Codes over F_p+vF_p and their Gray Images
In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes share similar properties with quadratic residue codes over finite fields. For the case p = 2, Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two...
متن کاملSome Results on Linear Codes over $\mathbb{Z}_4+v\mathbb{Z}_4$
In this paper, we study the linear codes over the commutative ring R = Z4 + vZ4, where v2 = v. We define the Gray weight of the elements of R and give a Gray map from Rn to Z2n 4 , which lead to the MacWillams identity of the linear code over R. Some useful results on self-dual code over R are given. Furthermore, the relationship between some complex unimodular lattices and Hermitian self-dual ...
متن کامل