add documentation fixes

README.md

@@ -39,7 +39,7 @@ pkg> add https://github.com/QuantumSavory/QuantumExpanders.jl.git
 
 To update, just type `up` in the package mode.
 
-The library provides the following methods to construct explicit instances of *Quantum Tanner codes*.
+The library provides the following methods to construct explicit instances of *quantum Tanner codes*.
 ```mermaid
 graph TD
     QuantumTannerCodes["Quantum Tanner Codes"] --> RandomMethods["Random Methods"]

docs/Project.toml

@@ -1,6 +1,7 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
+DocumenterMermaid = "a078cd44-4d9c-4618-b545-3ab9d77f9177"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 Hecke = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
 HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b"

docs/src/index.md

@@ -2,6 +2,23 @@
 
 A Julia library for constructing quantum Tanner codes and related expander-based quantum LDPC codes, built on top of [Oscar](https://www.oscar-system.org/), [QECCore](https://github.com/QuantumSavory/QECCore.jl), and [QuantumClifford](https://github.com/QuantumSavory/QuantumClifford.jl).
 
+The library provides the following methods to construct explicit instances of *quantum Tanner codes*.
+
+```mermaid
+graph TD
+    QuantumTannerCodes["Quantum Tanner Codes"] --> RandomMethods["Random Methods"]
+    QuantumTannerCodes --> DeterministicMethods["Deterministic Methods"]
+
+    subgraph "Random construction"
+        RandomMethods --> RandomQuantumTannerCode["`random_quantum_Tanner_code`"]
+    end
+
+    subgraph "Deterministic construction"
+        DeterministicMethods --> QuantumTannerCode["`QuantumTannerCode`"]
+        DeterministicMethods --> GeneralizedQuantumTannerCode["`GeneralizedQuantumTannerCode`"]
+    end
+```
+
 ## Quick Example
 
 Constructing a random quantum Tanner code from Morgenstern generators of ``SL_2(\mathbb{F}_4)``:

src/morgenstern.jl

@@ -243,11 +243,11 @@ specific set of ``q+1`` generators. These generators are ``2 \\times 2`` matrice
 where q = 2^l is an *even* prime power, and d is an even integer extension degree. The field ``\\mathbb{F}_{q^d}`` is
 constructed as ``\\mathbb{F}_q[x]/g(x)\\mathbb{F}_q[x]`` where g(x) is an irreducible polynomial of degree d. Within
 this field, ``\\mathbb{i}`` denotes a root of the irreducible polynomial ``x^2 + x + \\varepsilon = 0``. The pairs
-``(\\gamma_k, \\delta_k)`` are the q+1 solutions in `\\mathbb{F}_q^2`` to the ``\\gamma_k^2 + \\gamma_k\\delta_k + \\delta_k^2\\varepsilon = 1``.
+``(\\gamma_k, \\delta_k)`` are the q+1 solutions in ``\\mathbb{F}_q^2`` to the ``\\gamma_k^2 + \\gamma_k\\delta_k + \\delta_k^2\\varepsilon = 1``.
 And x is the polynomial variable that represents an element of ``\\mathbb{F}_{q^d}`` in the construction.
 
 The same theorem states that the resulting Cayley graph ``\\Gamma_g`` has the following properties: it is
-a (q+1)-regular Ramanujan graph of order ``|\\Gamma_g| = q^{3d} - q^d`` and is non-bipartite. The graph has
+a (``q+1``)-regular Ramanujan graph of order ``|\\Gamma_g| = q^{3d} - q^d`` and is non-bipartite. The graph has
 girth at least ``\\frac{2}{3}\\log_q|\\Gamma_g|`` and diameter at most ``2\\log_q|\\Gamma_g| + 2``. Furthermore,
 as per Theorem *5.11*, all eigenvalues ``\\mu`` of the adjacency matrix satisfy ``|\\mu| \\leq 2\\sqrt{q}`` for ``\\mu \\neq ``\\pm(q+1)``.
 

src/quantum_tanner_codes.jl

@@ -427,8 +427,8 @@ julia> code_n(c), code_k(c), distance(c, DistanceMIPAlgorithm(solver=HiGHS, logi
 ```
 
 !!! note
-    This is a newer version of the less well designed function `gen_code`(G, A, B, bipartite=true, use_same_local_code=false)`.
-    It constructs the quantum Tanner code given a finite group G equipped with two *symmetric* generating sets A and B,
+    This is a newer version of the less well designed function `gen_code(G, A, B, bipartite=true, use_same_local_code=false)`.
+    It constructs the quantum Tanner code given a finite group ``G`` equipped with two *symmetric* generating sets ``A`` and ``B``,
     alongside pairs of classical codes — comprising parity check and generator matrices — that are utilized in the
     construction of classical Tanner codes. To illustrate its application, the implementation can employ generating
     sets computed from the Morgenstern's explicit construction of Ramanujan graphs for odd prime power `q` generating sets.