MinT - Information on Result #1300612

Information on Result #1300612

Linear OA(4¹⁸⁵, 229, F₄, 96) (dual of [229, 44, 97]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹⁸⁴, 227, F₄, 96) (dual of [227, 43, 97]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹⁸³, 225, F₄, 96) (dual of [225, 42, 97]-code), using
    - 3 times truncation [i] based on linear OA(4¹⁸⁶, 228, F₄, 99) (dual of [228, 42, 100]-code), using
      - concatenation of two codes [i] based on
        linear OA(64²⁴, 38, F₆₄, 24) (dual of [38, 14, 25]-code or 38-arc in PG(23,64)), using
        discarding factors / shortening the dual code based on linear OA(64²⁴, 64, F₆₄, 24) (dual of [64, 40, 25]-code or 64-arc in PG(23,64)), using
        Reedâ€“Solomon code RS(40,64) [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(4¹⁸³, 226, F₄, 95) (dual of [226, 43, 96]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁸³Â > V_b^sâˆ’1(kâˆ’1)Â = 126 517424 059378 057638 374967 330631 374054 007832 559173 473691 562748 465533 157082 309010 349368 626378 265753 562249 391380 [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, 228, F₄, 95) (dual of [228, 44, 96]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁸⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 368 026314 164468 171666 840213 803132 404189 570936 819616 930417 279811 123287 546583 854340 368779 609459 410092 485948 337480 [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.