MinT - Information on Result #2244393

Information on Result #2244393

Linear OA(4²³⁷, 423, F₄, 80) (dual of [423, 186, 81]-code), using 1 times truncation based on linear OA(4²³⁸, 424, F₄, 81) (dual of [424, 186, 82]-code), using

concatenation of two codes [i] based on
1. linear OA(64⁴⁴, 106, F₆₄, 40) (dual of [106, 62, 41]-code), using
  - constructionÂ X applied to AG(F,62P) âŠ‚ AG(F,64P) [i] based on
    1. linear OA(64⁴³, 103, F₆₄, 40) (dual of [103, 60, 41]-code), using algebraic-geometric code AG(F,62P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]
    2. linear OA(64⁴¹, 103, F₆₄, 38) (dual of [103, 62, 39]-code), using algebraic-geometric code AG(F,64P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (see above)
    3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(4²³⁹, 425, F₄, 80) (dual of [425, 186, 81]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(4²³⁷, 211, F₄, 2, 80) (dual of [(211, 2), 185, 81]-NRT-code)	[i]	OOA Folding
3	Linear OOA(4²³⁷, 141, F₄, 3, 80) (dual of [(141, 3), 186, 81]-NRT-code)	[i]	OOA Folding