Hamming　space　retrieval　enables　efficient　constant-time　search　through　hash　table　lookups　constructed　by　hash　codes,　where　in　response　to　each　query,　all　data　points　within　a　small　given　Hamming　radius　are　returned　as　relevant　data.　However,　in　Hamming　space　retrieval,　the　search　performance　of　the　existed　hashing　schemes　based　on　linear　scan　dropped　when　the　length　of　the　hash　codes　increases.　The　reason　is　that　the　Hamming　space　becomes　very　sparse　and　it　is　difficult　to　pull　the　similar　data　into　the　Hamming　ball　and　to　push　the　dissimilar　data　outside　the　ball.　Currently,　the　existing　deep　hashing　methods　based　on　hash　table　lookups　pay　too　much　attention　to　similar　samples　outside　the　ball　and　ignore　the　learning　of　dissimilar　samples　inside　the　ball,　leading　to　a　biased　model.　In　this　paper,　we　introduce　discriminatory　penalty　into　the　exponential　loss　functions　to　optimize　the　Hamming　space,　leading　to　Exponential　Hashing　with　Discriminatory　Penalty　(EHDP),　which　discriminately　penalizes　similar/dissimilar　data　inside　and　outside　the　Hamming　ball.　Technically,　EHDP　capitalizes　on　exponential　function　to　discriminatively　encourage　similar/dissimilar　data　approaching/away　and　to　up-weight/down-weight　the　dissimilar　data　inside/outside　the　ball.　Extensive　experiments　demonstrate　that　the　proposed　EHDP　obtains　superior　results　on　three　benchmark　datasets.　©　2021,　Springer　Nature　Switzerland　AG.