Let C Fn 2 be a non-empty binary code. Define the following quantities: R+(C) = max...

 

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Let C✓ Fn 2 be a non-empty binary code. Define the following quantities: R+(C) = max x2Fn 2 min c2C d(x, c), R(C) = min x2Fn 2 max c2C d(x, c). Prove that R+(C) + R(C) = n. Let C be an [n, k, d] code over Fq. Prove or disprove the following claim: In any coset of C with a coset leader of weight >floor( (d-1)/2), the cost leader is not unique. Let C✓ Fn 2 be a non-empty binary code. Define the following quantities: R+(C) = max x2Fn 2 min c2C d(x, c), R(C) = min x2Fn 2 max c2C d(x, c). Prove that R+(C) + R(C) = n. Let C be an [n, k, d] code over Fq. Prove or disprove the following claim: In any coset of C with a coset leader of weight >floor( (d-1)/2), the cost leader is not unique.