Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes
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....
محفوظ في:
| المؤلفون الرئيسيون: | , |
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| مؤلفون آخرون: | |
| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
2013
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| الوصول للمادة أونلاين: | https://hdl.handle.net/10356/95846 http://hdl.handle.net/10220/11432 |
| الوسوم: |
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| المؤسسة: | Nanyang Technological University |
| اللغة: | English |
| الملخص: | 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. |
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