🔍minor formatting

Author: Fe-r-oz

test/Classical/quasi-cyclic_code_test.jl

@@ -29,21 +29,9 @@
             3,
             5,
             [
-                x,
-                x^2,
-                x^4,
-                x^8,
-                x^16,
-                x^5,
-                x^10,
-                x^20,
-                x^9,
-                x^18,
-                x^25,
-                x^19,
-                x^7,
-                x^14,
-                x^28,
+                x x^2 x^4 x^8 x^16;
+                x^5 x^10 x^20 x^9 x^18;
+                x^25 x^19 x^7 x^14 x^28
             ],
         )
         # A = matrix(R, 3, 5,

test/testcases.jl

@@ -123,3 +123,10 @@ C ∩ B == C
 B = BCHCode(q, n, δ - 1, b + 4)
 D = C ∩ B # check later that this is == repetition code
 C + B
+
+# Remove?
+# We will only be concerned with cyclic Reed-Solomon codes, but the more general, and original, definition of Reed-Solomon codes will lead us into the final family of codes we will use in this work. Let $\mathcal{P}_k(x)$ denote the set of polynomials of degree less than $k$ in $\mathbb{F}_{p^m}[x]$. The Reed-Solomon code of length $n \leq p^m$ and dimension $k < n$ is given by
+# 
+# $$\mathrm{RS}_{p^m}(n, k) = \{ (f(\alpha_1), \dots, f(\alpha_n)) \mid f(x) \in \mathcal{P}_k(x)\},$$
+# 
+# where $\alpha_i \in \mathbb{F}_{p^m}$. The most common case $n = p^m$ is the extended code of the cyclic definition, but only the case $n = p^m -1$ is, in general, cyclic. The proof of this is direct application of the Chinese Remainder Theorem.

test/utils_test.jl

@@ -278,60 +278,12 @@
         6,
         9,
         [
-            1,
-            0,
-            0,
-            0,
-            0,
-            0,
-            1,
-            1,
-            0,
-            0,
-            1,
-            0,
-            0,
-            0,
-            0,
-            0,
-            1,
-            1,
-            0,
-            0,
-            1,
-            0,
-            0,
-            0,
-            1,
-            0,
-            1,
-            1,
-            0,
-            1,
-            1,
-            1,
-            1,
-            0,
-            1,
-            0,
-            1,
-            1,
-            0,
-            1,
-            1,
-            1,
-            0,
-            0,
-            1,
-            0,
-            1,
-            1,
-            1,
-            1,
-            1,
-            1,
-            0,
-            0,
+            1 0 0 0 0 0 1 1 0;
+            0 1 0 0 0 0 0 1 1;
+            0 0 1 0 0 0 1 0 1;
+            1 0 1 1 1 1 0 1 0;
+            1 1 0 1 1 1 0 0 1;
+            0 1 1 1 1 1 1 0 0
         ],
     )
     @test weight_matrix(A) == [1 0 2; 2 3 1]