Computing the Spectrum of a Binary Group Code*

Abstract

The weight distribution of the code vectors of a binary group code has been referred to as the spectrum of the code. This paper presents a technique for calculating the spectrum of such a code, the spectra of shortened codes obtainable from the code, and what are defined as the level weight structures of the code. The method is conceptually straightforward and readily adaptable to digital computers. It involves operations no more complex than the addition of two (n − k)-tuples, the determination of the weight of certain (n − k)-tuples, and the ordinary addition of certain integers. Its computational complexities are independent of the code parameters. In principle, it may be used for any binary group code, but it is particularly useful for codes in which the number of parity check positions per code vector is rather small although the number of information positions may be large.