MinT - Information on Result #1300821

Information on Result #1300821

Linear OA(4²⁰⁹, 259, F₄, 108) (dual of [259, 50, 109]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4²⁰⁸, 257, F₄, 108) (dual of [257, 49, 109]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4²⁰⁷, 255, F₄, 108) (dual of [255, 48, 109]-code), using
    - 3 times truncation [i] based on linear OA(4²¹⁰, 258, F₄, 111) (dual of [258, 48, 112]-code), using
      - concatenation of two codes [i] based on
        linear OA(64²⁷, 43, F₆₄, 27) (dual of [43, 16, 28]-code or 43-arc in PG(26,64)), using
        discarding factors / shortening the dual code based on linear OA(64²⁷, 64, F₆₄, 27) (dual of [64, 37, 28]-code or 64-arc in PG(26,64)), using
        Reedâ€“Solomon code RS(37,64) [i]
        linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
        hyperoval in PG(2,Â 4) [i]
        the Hexacode [i]
  2. linear OA(4²⁰⁷, 256, F₄, 107) (dual of [256, 49, 108]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²⁰⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 37663 512109 235954 588572 164890 499827 076260 505880 044645 597059 470938 457717 831673 731331 645048 142890 710455 618731 581087 891915 434739 [i]
  3. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
linear OA(4²⁰⁸, 258, F₄, 107) (dual of [258, 50, 108]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²⁰⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 108966 631638 950353 960562 258813 086437 882960 037111 154920 267879 526645 521398 695244 402654 111182 268494 788261 931915 067055 835302 129204 [i]
linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code) (see above)

Mode: 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

None.