Abstract
Chor, Fiat and Naor proved a significant sufficient condition for traceability codes that an error correcting code of high minimum distance is a traceability code. Their result has been the basis of most constructions of traceability codes since then. This paper improves their result by showing that an error correcting code under a weaker requirement of minimum distance is still a traceability code by taking into account the effect of intersection of codewords. Furthermore, we show that the proposed weaker sufficient condition can be attained on 2-traceability codes by a new construction based on resolvable affine planes. In particular, this leads to a q-ary 2-traceability code of length 4 containing 3q codewords; moreover, we prove that the size 3q is optimal.
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