1. A parallel data encoding/decoding system which performs parallel data transmission from an encoder to a decoder using a plurality of lanes, the number of the plurality of lanes being R, R being an integer that is larger than or equal to 2,wherein the encoder generates a code vector M having R elements, each element of the code vector M is a symbol to be transmitted in parallel using the plurality of lanes, the code vector M being denoted M={m0, m1, m2, . . . mR?1|mi?GF(2n)}, m0, m1, m2, . . . mR?1 being the elements of the code vector M, GF(2n) being an n-order extension field of a Galois field, the number of the elements being equal to the number of the plurality of lanes, and the state vector U having R elements, each element in the state vector U is a code indicating to the decoder whether each of the corresponding elements of the code vector M is valid or invalid, the state vector U being denoted as U=(u0, u1, u2, . . . uR?1|ui?{0, 1}), u0, u1, u2, . . . uR?1 being the elements of the state vector U,

calculates products {m0u0, m1u1, m2u2, . . . , mR?1uR?1|mi?M, ui?U} of the elements of the code vector M and the elements of the state vector U,

generates a transmission vector Y by encoding the calculated products using a maximum distance separable (2R, R) block code with which erasure of R symbols is capable of being corrected,

transmits the transmission vector Y through the plurality of lanes, and

transmits the state vector U through the plurality of lanes or a path separate from the plurality of lanes,

the encoder comprises an MDS encoding computer that performs the encoding of the calculated products using the maximum distance separable (MDS) block code, and

the decoder decodes a subset Msub of the code vector M, the subset Msub being constituted of a valid element of the code vector M, using a received reception vector Y?, the received state vector U, and an erasure vector E indicating whether each element of the transmission vector Y has been erased in a transmission/reception section.