List Decoding of Quaternary Codes in the Lee Metric

We present a list decoding algorithm for quaternary negacyclic codes over the Lee metric. To achieve this result, we use a Sudan-Guruswami type list decoding algorithm for Reed- Solomon codes over certain ring alphabets. Our decoding strategy for negacyclic codes over the ring ${\mathbb{Z}_4}$ combines the list decoding algorithm by Wu with the Gröbner basis approach for solving a key equation due to Byrne and Fitzpatrick.