Sparse Regression Codes (SPARC) are error control codes which use sparse linear combinations of columns of a dictionary matrix as codewords. SPARC combines the sparse signal recovery framework of compressive sensing with error control coding techniques. SPARC is known to be asymptotically capacity achieving but has not been studied for the short block length regime. Considering the short block length regime, we construct dictionary matrices using Gold codes and mutually unbiased bases and develop suitable generalizations of SPARC to get better error performance. These generalizations include Sub-block Structure Encoding and Sub-block Free Encoding. We also develop a simple Match And Decode (MAD) decoder and improve its performance using parallelization resulting in Parallel MAD (PMAD) decoder. We show numerically that PMAD decoder outperforms classic recovery techniques such as OMP and AMP decoders and performs comparable to existing linear error control codes for short block lengths. We describe the applicability of SPARC with PMAD decoding for multi-user channels, resulting in non-orthogonal multiple access schemes. We also show that our codes outperform the lower bound for orthogonal multiple access codes in the short block length regime.