Lower bounds of dimension of linear codes for CDMA

A linear code of the length $2^n$ is called a saving property bent code (SPB-code) for a bent function $f$ if for any element $a$ of the code, $f(x\oplus a)$ is a bent function. For every bent function from Maiorana–McFarland class with $2n$ variables, there exists SPB-code of the dimension $2^{n+1}-1$. For every bent function with a linearity index $k$, there exists SPB-code of the dimension $2^{k+1}-1$.