The system of weight equations for a binary $(n, m)$-code with respect to its ordered basis is introduced. It connects certain quantities (characteristics) related to the basis with the weights of non-zero words in the code. It is shown that the portion involving the variables does not depend neither on the code nor on the basis. Explicit forms of the matrix of coefficients in the system and its inverse matrix are computed.
AKYILDIZ, ERSAN; GÜLOĞLU, İSMAİL Ş.; and IKEDA, MASATOSHI (1999) "The Weight Equations for Binary Linear Codes," Turkish Journal of Mathematics: Vol. 23: No. 4, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol23/iss4/2