Byte weight enumerators of codes over 𝔽p and modular forms over a totally real field
Anuradha Sharma, Amit Kumar Sharma · International Journal of Information and Coding Theory · 2017
In this paper, we obtain Jacobi forms over kp from byte weight enumerators of self-dual codes over 𝔽p, where p is an odd prime, kp is the totally real field of the pth cyclotomic field and 𝔽p is the finite field of order p. We also determine Siegel modular forms of genus g (g ≥ 1 is an integer) over kp by substituting certain theta series into byte weight enumerators in genus g of self-dual codes over 𝔽p for all p ∈ 𝔓, where the set 𝔓 consists of all those odd primes p for which the ring of algebraic integers of kp is a Euclidean domain. Further, we define some partial Epstein zeta functions and derive their functional equation using the Mellin transform of the theta series.