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In order to protect public network data transmission from layer 1 attacks by malicious users, self-synchronous scramblers have come into widespread use. Such networks include those using ATM, packet over SONET (POS), and the new generic framing procedure (GFP). Unfortunately, self-synchronous descramblers cause error multiplication that can degrade the performance of the popular CRC error check codes. The paper analyzes this scrambler/CRC interaction, and then presents a new class of CRC-16 codes that are optimized for these applications.