Some authors consider that evolutionary search may be positively influenced by the use of redundant representations, whereas others note that the addition of random redundancy to a representation could be useless in optimization. Given this lack of consensus, two new families of redundant binary representations are developed in this paper. The first family is based on linear transformations and is considered non-neutral. The second family of representations is designed to implement neutrality, and is based on the mathematical formulation of error control codes. A study aimed at assessing the influence of redundancy and neutrality on the performance of a simple evolutionary hillclimber is presented. The (1+1)-ES is modeled using Markov chains and is applied to NK fitness landscapes. The results indicate that the phenotypic neighborhood induced by a redundant representation dominates the behavior of the algorithm, affecting the search more strongly than neutrality, and the representations with better performance on NK fitness landscapes do not exhibit extreme values of any of the indicators of representation quality commonly adopted in the literature.