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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 Sherman-Morrison-Woodbury formula. The resulting approach involves significantly less computational load compared to popular approaches like Conjugate Gradient (CG) method and the (traditional) Cholesky decomposition.