TY - JOUR
T1 - Complete weight enumerators of a new class of linear codes
AU - Liu, Yiwei
AU - Liu, Zihui
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/7
Y1 - 2018/7
N2 - For an odd prime p, let q=pm, and denote Tre m the trace function from Fq onto Fpe , where e is a divisor of m. For a positive integer t and a∈Fpe , let Da={(x1,x2,…,xt)∈Fq t∖{(0,0,…,0)}:Tre m(x1+x2+⋯+xt)=a}, and define a p-ary linear code CDa as CDa ={c(x1,x2,…,xt):(x1,x2,…,xt)∈Fq t}, where c(x1,x2,…,xt)=(Tr1 m(x1d1 2+x2d2 2+⋯+xtdt 2))(d1,d2,…,dt)∈Da . The complete weight enumerators of linear codes CDa will be presented for any divisor e of m and a∈Fpe , and this new result generalizes that of both Ahn et al. (2017) and Yang et al. (2017).
AB - For an odd prime p, let q=pm, and denote Tre m the trace function from Fq onto Fpe , where e is a divisor of m. For a positive integer t and a∈Fpe , let Da={(x1,x2,…,xt)∈Fq t∖{(0,0,…,0)}:Tre m(x1+x2+⋯+xt)=a}, and define a p-ary linear code CDa as CDa ={c(x1,x2,…,xt):(x1,x2,…,xt)∈Fq t}, where c(x1,x2,…,xt)=(Tr1 m(x1d1 2+x2d2 2+⋯+xtdt 2))(d1,d2,…,dt)∈Da . The complete weight enumerators of linear codes CDa will be presented for any divisor e of m and a∈Fpe , and this new result generalizes that of both Ahn et al. (2017) and Yang et al. (2017).
KW - Complete weight enumerators
KW - Defining set
KW - Exponential sum
KW - Gauss sum
KW - Trace function
UR - http://www.scopus.com/inward/record.url?scp=85045567702&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2018.03.025
DO - 10.1016/j.disc.2018.03.025
M3 - Article
AN - SCOPUS:85045567702
SN - 0012-365X
VL - 341
SP - 1959
EP - 1972
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 7
ER -