In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of first-order Reed-Muller codes with respect to the information sets introduced in [2]. Using this algortihm we improve considerably the number of errors we can correct in comparison with the known results in this topic.

翻译：本文描述了一种经典置换解码算法的变体，该算法可应用于任何关于特定信息集类型的仿射不变码。特别地，我们可将其应用于[2]中引入的信息集下的一阶Reed-Muller码族。使用该算法，我们显著提高了可纠正的错误数量，相较于该领域已知结果有大幅改进。