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An Examination Of Codewords With Optimal Merit Factor, Michael W. Cammarano, Anthony G. Kirilusha
An Examination Of Codewords With Optimal Merit Factor, Michael W. Cammarano, Anthony G. Kirilusha
Department of Math & Statistics Technical Report Series
We examine the codewords with best possible merit factor (minimum sum of squares of periodic autocorrelations) for a variety of lengths. Many different approaches were tried in an attempt to find construction methods for such codewords, or for codewords with good but non-optimal merit factors.
Integer Maxima In Power Envelopes Of Golay Codewords, Michael W. Cammarano, Meredith L. Walker
Integer Maxima In Power Envelopes Of Golay Codewords, Michael W. Cammarano, Meredith L. Walker
Department of Math & Statistics Technical Report Series
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 …
Octary Codewords With Power Envelopes Of 3∗2M, Katherine M. Nieswand, Kara N. Wagner
Octary Codewords With Power Envelopes Of 3∗2M, Katherine M. Nieswand, Kara N. Wagner
Department of Math & Statistics Technical Report Series
This paper examines codewords of length 2m in Z8 with envelope power maxima of 3 ∗ 2m. Using the general form for Golay pairs as a base, a general form is derived for the set of coset leaders that generate these codewords. From this general form it will be proven that there exists at least one element in the coset that achieves a power of 3 ∗ 2m for each m-even and m-odd case.