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We address the use of erasure correcting codes to overcome the false-alarm and non-detection impairments of sensing in opportunistic spectrum access schemes. Non transmitted data because of primary user (PU) activity, or data lost during collisions between primary and secondary user (SU) transmissions can be seen as erasures and recovered with the help of erasure correcting codes. While long codes are generally considered to that end (some hundreds or thousands of consecutive packets) we focus on short codes by taking advantage that their performance can be greatly improved by a proper choice of the parity check matrix. This solution provides a new degree of freedom for the choice of a functioning point on the receiver operating characteristic (ROC) curve.