4.46 Show that (012) 1020 0102 is a parity-check matrix for C3 in Exercise 4.41 and that 10001 01010 is a parity-check matrix for C in Exercise 4.41. Using these parity-check matrices and assuming complete decoding, construct a syndrome look-up table for each of C3 and C2. (09000) 4.41 List the cosets of each of the following q-ary linear codes: (a) q = 3 and C3 = {0000, 1010, 2020, 0101, 0202, 1111, 1212, 2121, 2222}, } (b) 9 = 2 and C2 = {00000, 10001, 01010, 11011, 00100, 10101, 01110, 11111}. 4.46 Show that (012) 1020 0102 is a parity-check matrix for C3 in Exercise 4.41 and that 10001 01010 is a parity-check matrix for C in Exercise 4.41. Using these parity-check matrices and assuming complete decoding, construct a syndrome look-up table for each of C3 and C2. (09000) 4.41 List the cosets of each of the following q-ary linear codes: (a) q = 3 and C3 = {0000, 1010, 2020, 0101, 0202, 1111, 1212, 2121, 2222}, } (b) 9 = 2 and C2 = {00000, 10001, 01010, 11011, 00100, 10101, 01110, 11111}