1 votes 1 votes 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 $q^{n}$ $q ^{t}$ $q^{-n}$ $q^{-t}$ Others ugcnetcse-jan2017-paper3 binary-codes + – go_editor asked Mar 24, 2020 edited Jun 24, 2020 by soujanyareddy13 go_editor 409 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes I think the answer is (B) A 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}} where {\displaystyle \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 Neeraj7375 answered Nov 1, 2017 Neeraj7375 comment Share Follow See all 2 Comments See all 2 2 Comments reply rsansiya111 commented Dec 14, 2022 reply Follow Share It seems like you are trying to describe a vector space over a finite field with q elements. The notation $\mathbb{F}_q^n$ denotes a vector space of dimension n over the field $\mathbb{F}_q$. This means that each element of the vector space is a list of n elements from the field $\mathbb{F}_q$. The field $\mathbb{F}_q$ is a set of q elements (usually taken to be the numbers 0 through q-1) that can be combined using the operations of addition, subtraction, and multiplication (just like the real numbers). 0 votes 0 votes rsansiya111 commented Dec 14, 2022 reply Follow Share Yes, that is correct. A linear code of length n and rank k is a subspace of the vector space $\mathbb{F}_q^n$ with dimension k. This means that it is a set of vectors (codewords) that can be combined using the vector space operations of addition and scalar multiplication, and that has k linearly independent basis vectors. The size of the code, or the number of codewords it contains, is equal to $q^k$. 0 votes 0 votes Please log in or register to add a comment.