Systematic encoding of the Varshamov-Tenengol'ts codes and the Constantin-Rao codes
Khaled Abdel-Ghaffar, Hendrik Christoffel Ferreira · IEEE Transactions on Information Theory · 1998
The maximum number of information bits that can be encoded systematically by the number-theoretic codes of Varshamov and Tenengol'ts (1965) is determined. This number is also studied for the more general class of the group-theoretic Constantin-Rao (1979) codes. Although these codes are at least as large as the Varshamov-Tenengol'ts codes, it is shown that the number of bits that can be systematically encoded using a Constantin-Rao code does not exceed the number of bits that can be systematically encoded using a Varshamov-Tenengol'ts code. In fact, in many cases, the largest Constantin-Rao code has the least number of bits that can be systematically encoded.