On the Hyper-Kloosterman Codes Over Galois Rings

Etienne TANEDJEU ASSONGMO
2020 Journal of Mathematics Research  
The Hyper-Kloosterman code was first defined over finite fields by Chinen-Hiramatsu, see (Chinen, & Hiramatsu, 2001). In the present paper we define the Hyper-Kloosterman codes over Galois rings R(pe;m). We show that this code is the trace of linear code over R(pe;m). By the Hyper-Kloostermann sums over Galois rings, we determine the Hamming weight of any codeword of this code over Galois rings.
doi:10.5539/jmr.v12n2p12 fatcat:6owfooxfovdxplw7lmuuune3uu