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3 votes
Accepted

Find the number of matrices over the finite field $\mathbb F_{19}$, whose minimal polynomial has a certain degree $m$.

This is in principle doable by casework on the generalized Jordan normal form / primary rational canonical form but for $M_5(\mathbb{F}_{19})$ I think it gets very tedious, probably too tedious for a ...
Qiaochu Yuan's user avatar
2 votes
Accepted

AES S-box as simple algebraic transformation

The notation $$s = \left(b \times 31_{10} \bmod{257_{10}}\right) \oplus 99_{10}$$ does correspond to a polynomial multiplication of $b$ times $f = 1+x+x^2+x^3+x^4 \in \mathbb F_{2}[x].$ Here $f$ is ...
Keplerto's user avatar
  • 503
1 vote

Can somebody prove my finding which I am proposing here as a conjecture regarding the binary BCH code?

Work in progress: Too long for a comment: Perhaps looking at the (nonzero) cycles of this code will help. The cyclic code's parity-check polynomial has two factors: a primitive polynomial $m_{10}(x)$ ...
Dilip Sarwate's user avatar

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