On efficient second-order spectral-null codes using sets of m1-balancing functions

A new efficient coding scheme is given for second-order spectral-null (2-OSN) codes. The new method applies the Knuth´s optimal parallel decoding scheme for balanced (i.e., 1-OSN) codes to the random walk method introduced by Tallini and Bose to design 2-OSN codes. If k ∈ IN is the length of a 1-OSN code then the new 2-OSN coding scheme has length n = k+r ∈ IN with an extra redundancy of r ≳ 2 log₂ k + (1/2) log₂ log₂ k - 0.674 check bits. The whole coding process requires O(n log n) bit operations and 0(n) bit memory elements.