Access functions to online databases like codetables.de

[Fe-r-oz]

Maybe adding a function that queries an online database (codetables.de) and returns the best-known code for a given set of parameters, along with its construction details. Inspired by Sage's Access functions to online databases for coding theory.

The website codetables.de provides comprehensive tables of the best-known linear codes over various finite fields, along with their construction details.

Julia implementation of Sage's functionality of accessing codetables.de

using HTTP
using Gumbo
using Cascadia

function best_linear_code_in_codetables(n::Int, k::Int, F::String; verbose::Bool=false)
    q_match = match(r"GF\((\d+)\)", F)
    if q_match === nothing
        throw(ArgumentError("Invalid finite field format. Expected format: GF(q), where q is an integer."))
    end
    q = parse(Int, q_match.captures[1])
    if !(q in [2, 3, 4, 5, 7, 8, 9])
        throw(ArgumentError("q (= $q) must be in [2, 3, 4, 5, 7, 8, 9]"))
    end
    base_url = "http://www.codetables.de/BKLC/BKLC.php"
    params = "?q=$q&n=$n&k=$k"
    url = base_url * params
    if verbose
        println("Querying URL: $url")
    end
    response = HTTP.get(url)
    if response.status != 200
        throw(IOError("Failed to retrieve data: HTTP status $(response.status)"))
    end
    html_content = String(response.body)
    document = parsehtml(html_content)
    pre_tags = eachmatch(sel"pre", document.root)
    if isempty(pre_tags)
        throw(IOError("Error parsing data: <PRE> tags not found in the response."))
    end
    pre_content = nodeText(pre_tags[1])
    return pre_content
end

function nodeText(node)
    text = ""
    for child in children(node)
        if isa(child, HTMLText)
            text *= child.text
        else
            text *= nodeText(child)
        end
    end
    return text
end

Output:

julia> n = 72
72

julia> k = 36
36

julia> F = "GF(2)"
"GF(2)"

julia> result = best_linear_code_in_codetables(n, k, F, verbose=true)
Querying URL: http://www.codetables.de/BKLC/BKLC.php?q=2&n=72&k=36
"Construction of a linear code [72,36,15] over GF(2):\n[1]:  [73, 36, 16] Cyclic Linear Code over GF(2)\n     CyclicCode of length 73 with generating polynomial x^37 + x^36 + x^34 + x^33 + x^32 + x^27 + x^25 + x^24 + x^22 + x^21 + x^19 + x^18 + x^15 + x^11 + x^10 + x^8 + x^7 + x^5 + x^3 + 1\n[2]:  [72, 36, 15] Linear Code over GF(2)\n     Puncturing of [1] at 1\n\nlast modified: 2002-03-20\n"

julia> println(result)
Construction of a linear code [72,36,15] over GF(2):
[1]:  [73, 36, 16] Cyclic Linear Code over GF(2)
     CyclicCode of length 73 with generating polynomial x^37 + x^36 + x^34 + x^33 + x^32 + x^27 + x^25 + x^24 + x^22 + x^21 + x^19 + x^18 + x^15 + x^11 + x^10 + x^8 + x^7 + x^5 + x^3 + 1
[2]:  [72, 36, 15] Linear Code over GF(2)
     Puncturing of [1] at 1

last modified: 2002-03-20

This feature is a fun addition that may not be strictly necessary 😅 Although, I have read some papers that use this database codetables.de so maybe researchers may want to have access to databases to query parameters, bounds on minimum distance, etc. It could be helpful when constructing quantum codes from classical seed codes. Thanks to Eric for bringing up this topic.

[Fe-r-oz]

I think the above code can be modified by changing the base URL to https://codetables.de/QECC.php. :) I found this out by clicking on the view page source option. This way, we can query the QECC database of codetables.de that is relevant to us :) Sage folks query the (best known linear code) BKLC.php database.

ping @Krastanov

So, the modified code is:

using HTTP
using Gumbo
using Cascadia

function best_quantum_code(n::Int, k::Int, q::Int; verbose::Bool=false)
    if !(q in [2, 3, 4, 5, 7, 8])
        throw(ArgumentError("q (= $q) must be in [2, 3, 4, 5, 7, 8]"))
    end
    if !(1 ≤ n ≤ 256)
        throw(ArgumentError("n (= $n) must be in the range 1 ≤ n ≤ 256"))
    end
    if !(0 ≤ k ≤ n)
        throw(ArgumentError("k (= $k) must be in the range 0 ≤ k ≤ n"))
    end

    # Correct base URL for quantum codes
    base_url = "https://codetables.de/QECC.php"
    params = "?q=$q&n=$n&k=$k"
    url = base_url * params

    if verbose
        println("Querying URL: $url")
    end

    response = HTTP.get(url)
    if response.status != 200
        error("Failed to retrieve data: HTTP status $(response.status)")
    end

    html_content = String(response.body)
    document = parsehtml(html_content)
    pre_tags = eachmatch(sel"pre", document.root)
    if isempty(pre_tags)
        error("Error parsing data: <PRE> tags not found in the response.")
    end

    pre_content = nodeText(pre_tags[1])
    return pre_content
end

function nodeText(node)
    text = ""
    for child in children(node)
        if isa(child, HTMLText)
            text *= child.text
        else
            text *= nodeText(child)
        end
    end
    return text
end

Output :)

julia> n = 8
8

julia> k = 3
3

julia> code_details = best_quantum_code(n, k, q, verbose=true)
Querying URL: https://codetables.de/QECC.php?q=4&n=8&k=3
"Construction of a [[8,3,3]] quantum code:\n[1]:  [[8, 3, 3]] quantum code over GF(2^2)\n     Construction from a stored generator matrix\n\n    stabilizer matrix:\n\n      [1 0 0 0 1 0 1 1|0 0 1 0 1 1 0 1]\n      [0 0 0 1 0 1 1 1|1 0 1 0 0 1 1 0]\n      [0 1 0 0 1 1 1 0|0 0 1 1 1 0 1 0]\n      [0 0 0 1 0 1 1 1|0 1 0 1 1 0 0 1]\n      [0 0 1 1 1 0 1 0|0 0 0 1 0 1 1 1]\n\nlast modified: 2005-06-24\n"

julia> println(code_details)
Construction of a [[8,3,3]] quantum code:
[1]:  [[8, 3, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix

    stabilizer matrix:

      [1 0 0 0 1 0 1 1|0 0 1 0 1 1 0 1]
      [0 0 0 1 0 1 1 1|1 0 1 0 0 1 1 0]
      [0 1 0 0 1 1 1 0|0 0 1 1 1 0 1 0]
      [0 0 0 1 0 1 1 1|0 1 0 1 1 0 0 1]
      [0 0 1 1 1 0 1 0|0 0 0 1 0 1 1 1]

last modified: 2005-06-24

The above code can be modified to calculate the query the _tables with bounds on quantum codes [[n,k,d]]q

[Krastanov]

Having some form of access to these resources would be very valuable but there are multiple issues:

• the license at codetables.de is not specified -- there might simply not be a permission to do so
• the extracted data should not be a string but the actual structured code
• it might make more sense to gather the complete data or to figure out whether there is a more direct access to the database instead of relying on parsing html pages
• there is no guarantee that the format of these html pages would not change subtly in the future

[Fe-r-oz]

Thanks so much for your wonderful comments!