ECC dictionary S

shortened code :

Suppose C is an [n,k,d] code over GF(q) and i is any integer satisfying 1 ≤ i ≤ n. The shortened code C'' at the coordinate i is the code having length n-1 obtained by projecting the subcode

{ c=(c₁,...,c_n) in C | c_i=0 }

onto the remaining coordinates.

spectrum:

If A_C(x,y) = Σ_i=0ⁿ A_ix^n-iyⁱ is the weight enumerator of C, where

A_i = |{ c in C | wt(c)=i}|

denotes the number of codewords of weight i, then the spectrum of C is the list of coefficients of A_C :

spec(C)=[A₀, ... , A_n].