ترغب بنشر مسار تعليمي؟ اضغط هنا

Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over $mathbb{Z}_{2q}$

69   0   0.0 ( 0 )
 نشر من قبل Tao Wang
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.



قيم البحث

اقرأ أيضاً

In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of Fujiwara~cite{fujiwara1} can be generalized to repeated root cyclic codes (RRCCs) such that QSCs are always obtained, which is not the case with simple root cyclic codes. The usefulness of this extension is illustrated via examples of infinite families of QSCs from repeated root duadic codes. Finally, QSCs are constructed from the product of cyclic codes.
Let $p$ be a prime number. Irreducible cyclic codes of length $p^2-1$ and dimension $2$ over the integers modulo $p^h$ are shown to have exactly two nonzero Hamming weights. The construction uses the Galois ring of characteristic $p^h$ and order $p^{ 2h}.$ When the check polynomial is primitive, the code meets the Griesmer bound of (Shiromoto, Storme) (2012). By puncturing some projective codes are constructed. Those in length $p+1$ meet a Singleton-like bound of (Shiromoto , 2000). An infinite family of strongly regular graphs is constructed as coset graphs of the duals of these projective codes. A common cover of all these graphs, for fixed $p$, is provided by considering the Hensel lifting of these cyclic codes over the $p$-adic numbers.
133 - Jian Gao , Yun Gao , Fang-Wei Fu 2014
Linear codes are considered over the ring $mathbb{Z}_4+vmathbb{Z}_4$, where $v^2=v$. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of Euclidean isod ual codes, unimodular complex lattices, MDS codes and MGDS codes over $mathbb{Z}_4+vmathbb{Z}_4$ are studied. Cyclic codes and quadratic residue codes are also considered. Finally, some examples for illustrating the main work are given.
137 - Weijun Fang , Fang-Wei Fu 2018
Let $p$ be a prime and let $q$ be a power of $p$. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters [ [[tq, t q-2d+2, d]]_{q} ] for any $1 leq t leq q, 2 leq d leq lfloor frac{tq+q-1}{q+1}rfloor+1$, and [ [[t(q+1)+2, t(q+1)-2d+4, d]]_{q} ] for any $1 leq t leq q-1, 2 leq d leq t+2$ with $(p,t,d) eq (2, q-1, q)$. Our quantum codes have flexible parameters, and have minimum distances larger than $frac{q}{2}+1$ when $t > frac{q}{2}$. Furthermore, it turns out that our constructions generalize and improve some previous results.
We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $mathbb{F}_4$ and $mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with stricly improved p arameters than the current record. In numerous other occasions we obtain quantum codes with best-known performance. For the qutrit ones we supply a systematic construction to fill some gaps in the literature.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا