Context : Type Ib/c supernovae ( SNe Ib/c ) have been investigated in several single-object studies ; however , there is still a paucity of works concerning larger , homogeneous samples of these hydrogen-poor transients , in particular regarding the premaximum phase of their light curves . Aims : In this paper we present and analyze the early-time optical light curves ( LCs , ugriz ) of 20 SNe Ib/c from the Sloan Digital Sky Survey ( SDSS ) SN survey II , aiming to study their observational and physical properties , as well as to derive their progenitor parameters . Methods : High-cadence , multiband LCs are fitted with a functional model and the best-fit parameters are compared among the SN types . Bolometric LCs ( BLCs ) are constructed for the entire sample . We also computed the black-body ( BB ) temperature ( T _ { BB } ) and photospheric radius ( R _ { ph } ) evolution for each SN via BB fits on the spectral energy distributions . In addition , the bolometric properties are compared to both hydrodynamical and analytical model expectations . Results : Complementing our sample with literature data , we find that SNe Ic and Ic-BL ( broad-line ) have shorter rise times than those of SNe Ib and IIb . The decline rate parameter , \Delta m _ { 15 } , is similar among the different subtypes . SNe Ic appear brighter and bluer than SNe Ib , but this difference vanishes if we consider host galaxy extinction corrections based on colors . Templates for SN Ib/c LCs are presented . Our SNe have typical T _ { BB } of \sim 10000 K at the peak and R _ { ph } of \sim 10 ^ { 15 } cm . Analysis of the BLCs of SNe Ib and Ic gives typical ejecta masses M _ { ej } \approx 3.6 - 5.7 M _ { \odot } , energies E _ { K } \approx 1.5 - 1.7 \times 10 ^ { 51 } erg , and M ( ^ { 56 } Ni ) \approx 0.3 M _ { \odot } . Higher values for E _ { K } and M ( ^ { 56 } Ni ) are estimated for SNe Ic-BL ( M _ { ej } \approx 5.4 M _ { \odot } , E _ { K } \approx 10.7 \times 10 ^ { 51 } erg , M ( ^ { 56 } Ni ) \approx 1.1 M _ { \odot } ) . For the majority of SNe Ic and Ic-BL , we can put strong limits ( < 2 - 4 days ) on the duration of the expected early-time plateau . Less stringent limits can be placed on the duration of the plateau for the sample of SNe Ib . In the single case of SN Ib 2006lc , a > 5.9 days plateau seems to be detected . The rising part of the BLCs is reproduced by power laws with index < 2 . For two events ( SN 2005hm and SN 2007qx ) , we find signatures of a possible shock break-out cooling tail . Conclusions : Based on the limits for the plateau length and on the slow rise of the BLCs , we find that in most of our SNe Ic and Ic-BL the ^ { 56 } Ni is mixed out to the outer layers , suggesting that SN Ic progenitors are de facto helium poor . The derived progenitor parameters ( ^ { 56 } Ni , E _ { K } , M _ { ej } ) are consistent with previous works .