MinT - Information on Result #2275145

Information on Result #2275145

Linear OA(4²⁴³, 426, F₄, 83) (dual of [426, 183, 84]-code), using 2 times code embedding in larger space based on linear OA(4²⁴¹, 424, F₄, 83) (dual of [424, 183, 84]-code), using

concatenation of two codes [i] based on
1. linear OA(64⁴⁵, 106, F₆₄, 41) (dual of [106, 61, 42]-code), using
  - constructionÂ X applied to AG(F,61P) âŠ‚ AG(F,63P) [i] based on
    1. linear OA(64⁴⁴, 103, F₆₄, 41) (dual of [103, 59, 42]-code), using algebraic-geometric code AG(F,61P) [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(64⁴², 103, F₆₄, 39) (dual of [103, 61, 40]-code), using algebraic-geometric code AG(F,63P) [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		This result only	Method
1	Linear OOA(4²⁴³, 142, F₄, 3, 83) (dual of [(142, 3), 183, 84]-NRT-code)	[i]		OOA Folding