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Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes

หน่วยงาน Nanyang Technological University, Singapore

รายละเอียด

ชื่อเรื่อง : Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes
นักวิจัย : Jin, Lingfei , Xing, Chaoping
คำค้น : -
หน่วยงาน : Nanyang Technological University, Singapore
ผู้ร่วมงาน : -
ปีพิมพ์ : 2554
อ้างอิง : Jin, L., & Xing, C. (2012). Euclidean and Hermitian Self-Orthogonal Algebraic Geometry Codes and Their Application to Quantum Codes. IEEE Transactions on Information Theory, 58(8), 5484-5489. , http://hdl.handle.net/10220/11432 , http://dx.doi.org/10.1109/TIT.2011.2177066
ที่มา : -
ความเชี่ยวชาญ : -
ความสัมพันธ์ : IEEE transactions on information theory
ขอบเขตของเนื้อหา : -
บทคัดย่อ/คำอธิบาย :

In the present paper, we show that if the dimension of an arbitrary algebraic geometry code over a finite field of even characteristic is slightly less than n/2-g with n being the length of the code and g being the genus of the base curve, then it is equivalent to an Euclidean self-orthogonal code. Previously, such results required a strong condition on the existence of a certain differential. We also show a similar result on Hermitian self-orthogonal algebraic geometry codes. As a consequence, we can apply our result to quantum codes and obtain some good quantum codes. In particular, we obtain a q-ary quantum [[q+1,1]]-MDS code for an even power q which is essential for quantum secret sharing.

บรรณานุกรม :
Jin, Lingfei , Xing, Chaoping . (2554). Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes.
    กรุงเทพมหานคร : Nanyang Technological University, Singapore.
Jin, Lingfei , Xing, Chaoping . 2554. "Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes".
    กรุงเทพมหานคร : Nanyang Technological University, Singapore.
Jin, Lingfei , Xing, Chaoping . "Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes."
    กรุงเทพมหานคร : Nanyang Technological University, Singapore, 2554. Print.
Jin, Lingfei , Xing, Chaoping . Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes. กรุงเทพมหานคร : Nanyang Technological University, Singapore; 2554.