Code division multiple access (CDMA) has become a widely adopted technology for wireless communications, particularly in mobile third generation systems (3G) and global positional system (GPS). In CDMA, a particular class of pseudonoise (PN) spreading codes yields a code-set Grammian with only two distinct eigenvalues. For these spreading codes, we propose a computationally efficient method for signal detection using Wiener filtering. Our approach relies on a matrix inversion step, where we gain in computational efficiency by using the ShermanMorrisonWoodbury formula. The resulting approach involves significantly less computational load compared to popular approaches like Conjugate Gradient (CG) method and the (traditional) Cholesky decomposition.