Solution Manual For Coding Theory San Ling

Coding Theory: A First Course, authored by San Ling and Chaoping Xing, is a widely respected textbook used in advanced undergraduate and graduate courses in mathematics, computer science, and telecommunications. The book provides a rigorous introduction to algebraic coding theory, covering linear codes, cyclic codes, BCH codes, Reed–Solomon codes, and more advanced topics like convolutional codes and cryptographically relevant codes.

The Solution Manual (often unofficially circulated as a companion document) contains detailed, step-by-step solutions to the numerous exercises found at the end of each chapter. These exercises range from computational problems (e.g., constructing generator matrices, calculating syndromes) to theoretical proofs (e.g., proving bounds like the Singleton bound or the Hamming bound, demonstrating properties of finite fields in code construction).

Worked example

Note: Point out interplay between perfect codes and equality in Hamming bound.

Worked example

Tip: For manual construction, compute minimal polynomials of powers using conjugacy sets.

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Code sketch

# pseudocode: compute min distance
def min_distance(G):
    n = G.num_cols()
    k = G.num_rows()
    minw = n+1
    for v in all_binary_vectors(k) excluding zero:
        c = v @ G mod 2
        minw = min(minw, weight(c))
    return minw