MDS and self-dual codes over rings
نویسندگان
چکیده
In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.
منابع مشابه
Constacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملConstruction of MDS self-dual codes over Galois rings
The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction of self-dual codes over Galois rings as a GF(q)-analogue of [20]. We give a necessary and sufficient condition on which the building-up construction holds. We construct MDS self-dual codes of lengths up to 8 over GR(3, 2), GR(3, 2) and GR(3, 2), and near-MDS self-du...
متن کاملConstructions of self-dual codes over finite commutative chain rings
We study self-dual codes over chain rings. We describe a technique for constructing new self-dual codes from existing codes and we prove that for chain rings containing an element c with c = −1 all self-dual codes can be constructed by this technique. We extend this construction to self-dual codes over principal ideal rings via the Chinese Remainder Theorem. We use torsion codes to describe the...
متن کاملMDS codes over finite principal ideal rings
The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual...
متن کاملNew MDS or near MDS self-dual codes over finite fields
The study of MDS self-dual codes has attracted lots of attention in recent years. There are many papers on determining existence of q−ary MDS self-dual codes for various lengths. There are not existence of q−ary MDS self-dual codes of some lengths, even these lengths < q. We generalize MDS Euclidean self-dual codes to near MDS Euclidean self-dual codes and near MDS isodual codes. And we obtain ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Finite Fields and Their Applications
دوره 18 شماره
صفحات -
تاریخ انتشار 2012