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Random access Aloha protocols have well documented merits in terms of simplicity and favorable delay-throughput trade-off under moderate bursty traffic loads. Short spreading codes have been used in conjunction with random access to endow Aloha with benefits originating from spread-spectrum communications. Instead of short, symbol-periodic spreading, this paper considers long pseudo-random (PN) packet-periodic sequences in the context of spread-Aloha and establishes that long PN codes increase the maximum stable throughput by reducing the probability of collisions. Relying on a dominant system approach, we analyze the resultant throughput and demonstrate that increasing the PN code length quickly transforms the collision-limited channel to an interference-limited one. In particular, we investigate how throughput depends on user load and packet length. Finally, we discuss synchronization issues and provide corroborating numerical results.