Name
Abstract | ||
|---|---|---|
A class of powerful $$q$$ q -ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $$q$$ q -ary block codes that encode $$k$$ k qudits of quantum information into $$n$$ n qudits and correct up to $$\\left\\lfloor (d_{x}-1)/2 \\right\\rfloor $$ ( d x - 1 ) / 2 bit-flip errors and up to $$\\left\\lfloor (d_{z}-1)/2 \\right\\rfloor $$ ( d z - 1 ) / 2 phase-flip errors. In many cases where the length $$(q^{2}-q)/2 \\le n \\le (q^{2}+q)/2$$ ( q 2 - q ) / 2 ≤ n ≤ ( q 2 + q ) / 2 and the field size $$q$$ q are fixed and for chosen values of $$d_{x} \\in \\{2,3,4,5\\}$$ d x ¿ { 2 , 3 , 4 , 5 } and $$d_{z} \\ge \\delta $$ d z ¿ ¿ , where $$\\delta $$ ¿ is the designed distance of the Xing---Ling (XL) codes, the derived pure $$q$$ q -ary asymmetric quantum CSS codes possess the best possible size given the current state of the art knowledge on the best classical linear block codes. |
Year | DOI | Venue |
|---|---|---|
2013 | https://doi.org/10.1007/s10623-013-9885-5 | Designs, Codes and Cryptography |
Keywords | DocType | Volume |
Asymmetric quantum codes,CSS codes,Vandermonde matrix,Xing–Ling codes,81P45,81P70,94B05 | Journal | 75 |
Issue | ISSN | Citations |
1 | 0925-1022 | 2 |
PageRank | References | Authors |
0.38 | 6 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| martianus frederic ezerman | 1 | 66 | 10.14 |
| Somphong Jitman | 2 | 57 | 14.05 |
| Patrick Solé | 3 | 636 | 89.68 |