Methods, systems, and devices for wireless communications are described. A wireless device such as a user equipment (UE) may identify a codebook matrix having a number of rows equal to a first number and a number of columns equal to a second number, the first number equal to a number of UEs supported for communication with a base station, and the second number equal to a sequence length of a set of UE specific signature sequences, where the rows of the codebook matrix comprise a Welch bound equality (WBE) achieving vector set. The UE may identify a UE specific signature sequence based at least in part on a mapping between an identifier associated with the UE to one or more rows of the codebook matrix, and communicate with the base station based at least in part on the UE specific signature sequence.