1.8 Supplementary Exercises ercise 1.12 Is there an instantaneous code over Z3 with word-lengths li =1, 2, 2, 2, 2, 2, 3, 3, 3, 3? Construct one with l -1,2,2,2,2,2,3,3,3, how many such codes are there? 1.13 The binary code C = {0, 10, 11) is used, how many code-sequences of length j can be formed from C? (Hint: find and solve a recurrence relation for this number Ny.) Exercise 1.14 Suppose that lTl = r, 1-11 -...-,, and r-k-1. In how many ways can one choose words w,..., wq T so that lwl and wi,..., wa) is an instantaneous code? ercise 145 A code is exhaustive if every sufficiently long sequence of code-symbols begins with a code-word (equivalently, every infinite sequence of code- symbols can be decomposed into code-words). Find an equivalent condition in terms of the leaves of the tree TS in the proof of Theorem 1.20. Which of the codes in the examples in this chapter are exhaustive? 1.8 Supplementary Exercises ercise 1.12 Is there an instantaneous code over Z3 with word-lengths li =1, 2, 2, 2, 2, 2, 3, 3, 3, 3? Construct one with l -1,2,2,2,2,2,3,3,3, how many such codes are there? 1.13 The binary code C = {0, 10, 11) is used, how many code-sequences of length j can be formed from C? (Hint: find and solve a recurrence relation for this number Ny.) Exercise 1.14 Suppose that lTl = r, 1-11 -...-,, and r-k-1. In how many ways can one choose words w,..., wq T so that lwl and wi,..., wa) is an instantaneous code? ercise 145 A code is exhaustive if every sufficiently long sequence of code-symbols begins with a code-word (equivalently, every infinite sequence of code- symbols can be decomposed into code-words). Find an equivalent condition in terms of the leaves of the tree TS in the proof of Theorem 1.20. Which of the codes in the examples in this chapter are exhaustive