DECODING GROUP CODE WITH GR¨O BNER BASES

In this paper we present Gr¨obner bases for group block codes in general forms, including binary and non-binary codes. Gr¨obner bases for binary linear codes is introduced by Borges et al.[2]. We extended their work to non-binary group block codes then define an ideal for a group code C. Using the reduced Gr¨obner bases for its ideal C and reduction process, a decoding algorithm is introduced. We implement this decoding method for lower dimensions