MinT - Information on Result #1300056

Information on Result #1300056

Linear OA(4¹¹³, 142, F₄, 59) (dual of [142, 29, 60]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹¹², 140, F₄, 59) (dual of [140, 28, 60]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹¹¹, 138, F₄, 59) (dual of [138, 27, 60]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(64¹⁴, 23, F₆₄, 14) (dual of [23, 9, 15]-code or 23-arc in PG(13,64)), using
        discarding factors / shortening the dual code based on linear OA(64¹⁴, 64, F₆₄, 14) (dual of [64, 50, 15]-code or 64-arc in PG(13,64)), using
        Reedâ€“Solomon code RS(50,64) [i]
      2. 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(4¹¹¹, 139, F₄, 58) (dual of [139, 28, 59]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹¹¹Â > V_b^sâˆ’1(kâˆ’1)Â = 6 001634 873871 474729 109069 262479 618892 349863 608498 111415 734442 341864 [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(4¹¹², 141, F₄, 58) (dual of [141, 29, 59]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹¹²Â > V_b^sâˆ’1(kâˆ’1)Â = 17 040794 782936 843137 560967 023866 120954 519458 266490 725306 371426 327384 [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.