MinT - Information on Result #1300614

Information on Result #1300614

Linear OA(4¹⁸⁵, 232, F₄, 95) (dual of [232, 47, 96]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹⁸⁴, 230, F₄, 95) (dual of [230, 46, 96]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹⁸³, 228, F₄, 95) (dual of [228, 45, 96]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(64²³, 38, F₆₄, 23) (dual of [38, 15, 24]-code or 38-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]
      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(4¹⁸³, 229, F₄, 94) (dual of [229, 46, 95]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁸³Â > V_b^sâˆ’1(kâˆ’1)Â = 144 245084 000677 070129 893784 558059 712944 437473 394461 400947 705536 639978 289095 960645 471435 277439 814814 332127 510920 [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(4¹⁸⁴, 231, F₄, 94) (dual of [231, 47, 95]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁸⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 406 049218 845643 984317 056426 494670 988740 305248 026255 661092 401674 775272 138402 830983 143200 054541 021664 737587 844940 [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.