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We investigate a code-constrained constant modulus (CM) design criterion for direct sequence code division multiple access (DS-CDMA) in frequency selective channels. We propose a closed-form solution for linear receivers based on constrained optimisation techniques that combine multipath signals using multiple constraints which are treated as variables and are jointly optimised with the receiver. We develop a code-constrained constant modulus (CCM) recursive least squares (RLS) type algorithm for jointly estimating the parameters of the channel and the receiver in order to suppress multi-access and intersymbol interference. Simulation experiments are carried out for various scenarios and show that the proposed CCM-RLS algorithm outperforms previously reported methods.