论文标题
关于1-fibonacci错误纠正代码的解码
On the decoding of 1-Fibonacci error correcting codes
论文作者
论文摘要
对新错误纠正代码的研究在过去几年中引起了人们的关注，尤其是因为它们在抗量子计算机上抗攻击的密码系统中使用。在2006年，在对未来的研究进行更深入的分析时，斯塔霍夫（Stakhov）就如何利用斐波那契数字提出了一些有趣的想法，以得出以紧凑的表示的原始错误纠正代码。在这项工作中，我们提供了一个明确的公式来计算Stakhov代码的冗余，我们确定了Stakhov所描述的初始解码程序中的一些流动，其关键点是解决一些非繁琐的双性苯胺方程，并提供有关如何在某些情况下避免在某些情况下避免解决这些方程式和检测和更有效的详细讨论的详细讨论。
The study of new error correcting codes has raised attention in the last years, especially because of their use in cryptosystems that are resistant to attacks running on quantum computers. In 2006, while leaving a more in-depth analysis for future research, Stakhov gave some interesting ideas on how to exploit Fibonacci numbers to derive an original error correcting code with a compact representation. In this work we provide an explicit formula to compute the redundancy of Stakhov codes, we identify some flows in the initial decoding procedure described by Stakhov, whose crucial point is to solve some non-trivial Diophantine equations, and provide a detailed discussion on how to avoid solving such equations in some cases and on how to detect and correct errors more efficiently.
