Geodesic
Codes over hyperfields
Discussiones Mathematicae. General Algebra and Applications, Tome 37 (2017) no. 2, pp. 147-160

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In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices. We also demonstrate that codes over finite Krasner hyperfields are more interesting for code theory than codes over classical finite fields.
Keywords: hypervector space, hyperring, hyperfield, linear code 
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     title = {Codes over hyperfields},
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Atamewoue Tsafack, Surdive; Ndjeya, Selestin; Strüngmann, Lutz; Lele, Celestin. Codes over hyperfields. Discussiones Mathematicae. General Algebra and Applications, Tome 37 (2017) no. 2, pp. 147-160. http://geodesic.mathdoc.fr/item/DMGAA_2017_37_2_a3/