Asymptotically good binary code with efficient encoding & Justesen code. Tomer Levinboim Error Correcting Codes Seminar (2008). Outline. Intro codes Singleton Bound Linear Codes Bounds Gilbert-Varshamov Hamming RS codes Code Concatention Examples Wozencraft Ensemble Justesen Codes.
Error Correcting Codes Seminar (2008)
* conflicting goals - would like to be able to construct an [n,k,d]q code s.t. δ>0, R>0 and both are constant.
Note: for clarity Cx means C(x)
RS meet the Singleton bound
*Madhu Sudan (Lecture 5, 2001)
* Luca Trevisan (Lecture 2)
such that (R=1/2) (
y in Ball(0n, d)
there are at most Vol(n,d) “bad” codes