Abstract This work presents a new decoding algorithm that extends the error-correction capacity of group testing based (GTB) non-binary error correction codes without modifying the number of parity symbols of the codeword. A list decoding algorithm based on the pattern of the syndromes takes advantage of the parity matrix equation exploiting its structure. The decoding algorithm can be reformulated by detecting superimposed errors (errors that affect to the same parity check equation). The list of superimposed patterns applies the extrinsic information of the non-superimposed locations to correct the errors. The list of non-superimposed locations simply apply a majority-logic pattern. The complexity of the proposed solution is lower, as it does not require complex operations such as multiplications or inversions in the Galois Field and shares the magnitude equations for both cases, keeping the rest of the equations with the same number of comparisons as the original single-symbol error correction algorithm.

中文翻译：

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基于最小距离d < 5的非二进制纠错码组测试的扩展符号纠错算法

摘要 这项工作提出了一种新的解码算法，可以在不修改码字奇偶校验符号数量的情况下，扩展基于组测试（GTB）的非二进制纠错码的纠错能力。基于校验子模式的列表解码算法利用奇偶矩阵方程的结构。可以通过检测叠加错误（影响相同奇偶校验等式的错误）来重新制定解码算法。叠加模式列表应用非叠加位置的外在信息来纠正错误。非叠加位置列表仅应用多数逻辑模式。所提出的解决方案的复杂性较低，