主 题: Counting Codes over Finite Rings
报告人: Fidel Nemenzo (University of the Philippines Diliman)
时 间: 2016-10-31 15：00-16：00
地 点: 理科1号楼1303
The usual setting for codes are the Galois fields but there has been
much interest in recent years in codes over the weaker structures of
finite rings. The reason for this growing interest is the discovery
that certain good codes over fields can be constructed in a natural
way from finite ring codes.
Codes of length n over a finite ring R are R-submodules of the
set R^n of n-tuples over R.
Self-dual codes are a special family of codes. A general problem is
that of classifying codes over the ring Z_m of integers
modulo m. Since the Chinese Remainder Theorem can be applied to such
codes, it is enough to consider codes modulo the prime powers.
Classification of codes is computationally difficult, but can be made
easier if there is a mass formula, which gives the total number of
codes of given length n. In this talk, I discuss recent work with on mass formulas
for the ring Z_m, as well as for other special rings.