Classification of Cosets of the Reed-Muller Code R(m - 3,m)
Xiang‐dong Hou · 2005
Abstract Cosets of the Reed-Muller code R ( m −3, m ) are classified under the actions of GL( m ,2) and GA( m ,2), the latter being the automorphism group of R ( m —3, m ) for m ⩾4. The number of cosets in each class is calculated. Orphans of R ( m −3, m ) are identified, and the normality of R ( m −3, m ) is established. A recursive formula is given for computing weight distributions of cosets of R ( m −3, m ). The formula gives the number of vectors of weight w in a coset of R ( m −3, m ) with minimal weight μ rather easily when w is not far away from μ.