In this paper, we present two variations on a linear physical-layer security code for the binary erasure wiretap channel, and examine their performance using small blocklength LDPC codes at rates above the secrecy capacity. We consider the maximum-likelihood attack, along with a message-passing attack, and show how the proposed codes enhance security in each case. Unique security metrics are employed for each attack algorithm as necessary to showcase the security enhancements of the new codes, which are built on the notion of random stopping-setconscious puncturing of encoded bits followed by the addition of sets of edges in the Tanner graph corresponding to the paritycheck matrix. The new codes are shown to provide enhanced security without decreasing the coding rate.

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