Nonsystematic perfect codes
Kevin T. Phelps, Mike LeVan · SIAM Journal on Discrete Mathematics · 1999
We investigate nonsystematic perfect binary codes of length n, establishing that nonsystematic perfect codes of length n exist for all admissible $n \geq 15$. This improves on the result of Avgustinovich and Solov'eva [ Proc. 5th Internat. Workshop Algebraic and Combinatorial Coding Theory, Cosopol, Bulgaria, 1996, pp. 15--19] who have established the existence of such codes for $n\geq 255$. We also provide the results of a computer investigation of nonsystematic perfect codes of length 15.