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A t-error correcting q-nary linear code satisfy :

$M\sum_{i=0}^{t}(\frac{n}{i})(q-1)^{i}\leq X$

Where M is the number of code words and X is

  1. $q^{n}$
  2. $q ^{t}$
  3. $q^{-n}$
  4. $q^{-t}$
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I think the answer is (B)

linear code of length n and rank k is a linear subspace C with dimension k of the vector space {\displaystyle \mathbb {F} _{q}^{n}}\mathbb {F} _{q}^{n} where {\displaystyle \mathbb {F} _{q}}\mathbb {F} _{q} is the finite field with q elements. Such a code is called a q-ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords. The size of a code is the number of codewords and equals qk

Reference:https://en.wikipedia.org/wiki/Linear_code

correct me if i am wrong

Answer:

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