From aa385baff9c0de9fc0bbe55a2b50dc5f7d85509e Mon Sep 17 00:00:00 2001 From: Alok Kumar Date: Fri, 13 Dec 2024 04:34:30 +0530 Subject: [PATCH] docs: correct errors in binius-01 article --- fri-binius/binius-01.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/fri-binius/binius-01.md b/fri-binius/binius-01.md index 6913b6f..b29ab49 100644 --- a/fri-binius/binius-01.md +++ b/fri-binius/binius-01.md @@ -101,7 +101,7 @@ $$ Let's denote the root of $f_1(X)$ in $\mathbb{F}_{2^4}$ as $\theta$, then any element $a\in\mathbb{F}_{2^4}$ can be uniquely represented as: $$ -a = a_0 + a_1\cdot\theta + a_2\cdot\theta^2 + \cdots + a_{n-1}\cdot\theta^{n-1} +a = a_0 + a_1\cdot\theta + a_2\cdot\theta^2 + a_3\cdot\theta^3 $$ To add here, $f_1(X)$ is also a Primitive polynomial, and its root $\theta$ is also a Primitive Element of $\mathbb{F}_{2^4}$. Note that not all irreducible polynomials are Primitive polynomials, for example, $f_3(X)$ listed above is not a Primitive polynomial. @@ -217,7 +217,7 @@ $$ \begin{array}{ccccccc} \hline 0000 & 0001 & 0010 & 0011 & 0100 & 0101 & 0110 & 0111 \\ -0 & 1 & \eta & \eta+1 & \zeta & \zeta+\eta & \zeta+\eta+1 & \zeta+\eta+1 \\ +0 & 1 & \eta & \eta+1 & \zeta & \zeta+1 & \zeta+\eta & \zeta+\eta+1 \\ \hline 1000 & 1001 & 1010 & 1011 & 1100 & 1101 & 1110 & 1111 \\ \zeta\eta & \zeta\eta + 1 & \zeta\eta + \eta & \zeta\eta + \eta + 1 & \zeta\eta + \zeta & \zeta\eta + \zeta +1 & \zeta\eta+\zeta+\eta & \zeta\eta+\zeta+\eta+1 \\