This paper examines the distribution of integer peaks amoung Golay cosets in Ζ4. It will prove that the envelope power of at least one element of every Golay coset of Ζ4 of length 2m (for m-even) will have a maximum at exactly 2m+1. Similarly it will be proven that one element of every Golay coset of Ζ4 of length 2m (for m-odd) will have a maximum at exactly 2m+1. Observations and partial arguments will be made about why Golay cosets of Ζ4 of length 2m (for m-even) contain no elements with such a peak.
Michael W. Cammarano and Meredith L. Walker. Integer Maxima in Power Envelopes of Golay Codewords. Technical paper (TR-99-01). Math and Computer Science Technical Report Series. Richmond, Virginia: Department of Mathematics and Computer Science, University of Richmond, April, 1999.