This paper improves the Finiasz-Vaudenay construction of TCHo, a hardware-oriented public-key cryptosystem, whose security relies in the hardness of finding a low-weight multiple of a given polynomial, and on the decoding of certain noisy cyclic linear codes. Our improvement makes it possible to decrypt in polynomial time (instead of exponential time), to directly prove semantic security (instead of one-wayness), and to achieve pretty good asymptotic performances. We further build IND-CCA secure schemes using the KEM/DEM and Fujisaki-Okamoto hybrid encryption frameworks in the random oracle model. This can encrypt an arbitrary message with an overhead of about 5 Kb in less than 15 ms, on an ASIC of about 10000 gates at 4 MHz.