The weight distribution of linear codes over GF(ql) having generator matrix over GF(q>)

Duality and Support Weight Distributions

“…Thisresultappearedfirstin [5]andwasformulatedasageneralizedMacWilliams identity in [6]. A different proof of this result appeared in [9].…”

“…Private correspondence with Aaron Gulliver, coauthor of the mentioned talk, has been very valuable during the research. Finally, I wish to thank Torleiv Kløve for his continuous advice as a supervisor, concerning presentation and publication, and also for his help in finding and understanding [5]. The authors are with the Politecnico di Torino, 10129 Torino, Italy (e-mail:…”

Weight distributions of geometric Goppa codes

“…Let K be the function field of the curve defined by y 2 + y = x 5 over F 16 . The field K has 33 rational places; hence it is maximal with zeta-function Z K (T ) = (1 + 4T ) 4 /(1 − T )(1 − 16T ).…”

“…The group Γ is elementary abelian of order 625. An elementary way, though not the shortest way, to see that Γ is annihilated by five involves functions of the type y above, for a, b ∈ F 16 . Table 1 gives the order of the automorphisms and the number of fixed points.…”

“…The zeta function Z L (T ), for a constant field extension L/K, is determined by the zeta function Z K (T ). For a given code C, the weight distribution does in general not determine the weight distribution after a constant field extension [16]. It does suffice however to consider finitely many constant field extensions.…”