A class of low-rate nonlinear binary codes

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This paper introduces a new class of nonlinear binary codes. For each l = 2, 3,… we present a code with 241 codewords of length N = 4l and distance d = (4l — 2l)/2. Each code is a supercode of the 1st-order Reed-Muller (RM) code and a subcode of the 2nd-order RM code. These codes are the “duals≓ of the extended nonlinear Preparata codes in the sense that their weight distributions satisfy the MacWilliams identities.

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This research was partially supported by the Air Force Office of Scientific Research (AFSC) under Contract F44620-71-C-0001. This paper is based upon portions of a dissertation submitted in 1972 to the Faculty of the Polytechnic Institute of Brooklyn, in partial fulfillment of the requirements for the Ph.D. degree in electrical engineering.