On the Number of Minimum Weight Codewords of Subcodes of Reed-Muller Codes

摘要

In this paper, we consider linear subcodes of RM_r,m whose bases are formed from the monomial basis of RM_r,m by deleting ΔK monomials in order to obtain a subcode with (m r). For such subcodes, a procedure for computing the num- ber of minimum weight codewords is presented and it is shown how to delete ΔK monomials in order to obtain a subcode with the smallest number for the number of codewords of the mini- ΔK ≤ 3, a formula for the number f codewords of the mini- mum weight is presented. A (64,40) subcode of RM_3,6 is being considered as an inner code in a concatenated coding system for NASA's high-speed satellite communications.