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A new class of multiple access algorithms for systems without feedback is introduced and analyzed. A finite population of users is assumed, where each user transmits a packet R times within the next N time slots (and all packets have an equal length of one slot). To improve the performance achieved by randomly selecting these R slots, user codes are invoked such that any two users will only transmit simultaneously in at most one slot, i.e., 2-(N, R, 1) designs. We argue that in most cases, the set of user codes can be generated easily using cyclic designs and provide a method to select T user codes from the set of user codes SN,R in case the user population consists of T < |SN,R| users. We further demonstrate how larger populations, with T > |SN,R|, can still benefit from these user codes in two different manners. Closed formulas that express the success probability of a packet are provided for all population setups. Finally, a comparison with the random selection strategy demonstrates the performance gain realized by the new multiple access algorithms and some engineering rules to optimize the performance are provided.