On efficient m-ary q-th order spectral-null codes

Let S(N,q,m) be the set of all words of length N over the m-ary alphabet Φ_m={-(m-1),-(m-3),…,+(m-3),…,+(m-1)} having a q-th order spectral-null at zero frequency. Any subset of S(N,q,m) is a m-ary q-th order spectral-null code. This paper presents a new efficient method to encode k information m-ary digits into a m-ary second-order spectral-null code whose redundancy is ⩽3log_mk+O(loglogk); for all values of m⩾2