Construction of single-deletion-correcting DNA codes using CIS codes

초록

We find a method for constructing DNA codes with single-deletion-correcting capability. We first present an explicit algorithm for the construction of theq-ary single-deletion-correcting codes (abbreviated asSDC codes) using a class of the complementary information set codes (abbreviated asCIS codes), whereqis a power of a prime. We then show that the encoding/decoding scheme of the CIS codes with single-deletion-correcting capability has a simple deterministic algorithm. Finally, applying our algorithm to the generated DNA codes with appropriate modification, we obtain the DNA codes with single-deletion-correcting capability. We present some various examples of such DNA codes, and we also obtain some lower bounds on the maximum size of the single-deletion-correcting DNA codes.

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