MinT - Information on Result #1300551

Information on Result #1300551

Linear OA(4¹⁸⁰, 224, F₄, 93) (dual of [224, 44, 94]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹⁷⁹, 222, F₄, 93) (dual of [222, 43, 94]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹⁷⁸, 220, F₄, 93) (dual of [220, 42, 94]-code), using
    - 2 times truncation [i] based on linear OA(4¹⁸⁰, 222, F₄, 95) (dual of [222, 42, 96]-code), using
      - concatenation of two codes [i] based on
        linear OA(64²³, 37, F₆₄, 23) (dual of [37, 14, 24]-code or 37-arc in PG(22,64)), using
        discarding factors / shortening the dual code based on linear OA(64²³, 64, F₆₄, 23) (dual of [64, 41, 24]-code or 64-arc in PG(22,64)), using
        Reedâ€“Solomon code RS(41,64) [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(4¹⁷⁸, 221, F₄, 92) (dual of [221, 43, 93]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁷⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 115781 416850 000767 391926 036290 533873 431590 760235 965882 936709 978786 129243 959556 507163 365153 210543 001493 724617 [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(4¹⁷⁹, 223, F₄, 92) (dual of [223, 44, 93]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁷⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 332050 208768 443913 268349 022488 139107 567746 229615 633242 982860 546594 856631 809120 990964 799603 097536 763476 392998 [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.