# Tagged Questions

Finite fields are structures arising in abstract algebra. The order of a finite field is always a prime power, and for each prime power $q$ there is a single isomorphism type. It is usually denoted by $\mathbb{F}_q$ or $\operatorname{GF}(q)$.

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### generalization of positive-definite matrices to matrices over finite fields

Let $\mathbb{F}$ be a field, $\mathbb{F}^n$ be the $n$-dimensional vector space over $\mathbb{F}$, and $M_{n\times n}(\mathbb{F})$ be the space of $n\times n$ matrices with entries in $\mathbb{F}$. We ...
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### Probability that an arbitrary element of a field has a specific structure.

This question is related to : http://crypto.stackexchange.com/questions/37351/encoding-an-element-in-r-rhr-way that I asked couple of weeks ago. The difference is that I did not take the collision ...
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### Extending a code by adding a parity check

Let $C$ be a $[n,k,d]_2$ code where $d$ is odd. It is known that you can construct a $[n+1,k,d+1]_2$ code by adding a column $\boldsymbol{c}_{n+1}$ to the codebook matrix where each element contains ...
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