Quantum codes from cyclic codes over GF(4m)
نویسندگان
چکیده
We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF (4)) starting from cyclic codes over GF (4). We also provide examples of these codes some of which meet the known bounds for quantum codes.
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 کاملOptimal Linear Codes Over GF(7) and GF(11) with Dimension 3
Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...
متن کاملSkew Generalized Quasi-cyclic Codes
This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...
متن کاملAnother q-Polynomial Approach to Cyclic Codes
c0 + c1x+ c2x 2 + · · ·+ cn−1x n−1 ∈ GF(q)[x]/(x − 1), any code C of length n over GF(q) corresponds to a subset of the quotient ring GF(q)[x]/(xn− 1). A linear code C is cyclic if and only if the corresponding subset in GF(q)[x]/(xn − 1) is an ideal of the ring GF(q)[x]/(xn − 1). It is well known that every ideal of GF(q)[x]/(xn−1) is principal. Let C = 〈g(x)〉 be a cyclic code, where g(x) is m...
متن کاملClassification of Hermitian self-dual additive codes over GF(9)
Abstract—Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes have so far received far less interest from coding theorists than self-dual additive codes over GF(4), which correspond to binary quantum codes. Self...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 47 شماره
صفحات -
تاریخ انتشار 2001