MinT - Information on Result #1300377

Information on Result #1300377

Linear OA(4¹⁶¹, 202, F₄, 83) (dual of [202, 41, 84]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹⁶⁰, 200, F₄, 83) (dual of [200, 40, 84]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹⁵⁹, 198, F₄, 83) (dual of [198, 39, 84]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(64²⁰, 33, F₆₄, 20) (dual of [33, 13, 21]-code or 33-arc in PG(19,64)), using
        discarding factors / shortening the dual code based on linear OA(64²⁰, 64, F₆₄, 20) (dual of [64, 44, 21]-code or 64-arc in PG(19,64)), using
        Reedâ€“Solomon code RS(44,64) [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(4¹⁵⁹, 199, F₄, 82) (dual of [199, 40, 83]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁵⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 494195 258011 714927 659805 629377 341174 214295 512048 812481 802748 943012 074511 417935 935074 586501 510424 [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(4¹⁶⁰, 201, F₄, 82) (dual of [201, 41, 83]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹⁶⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 1 393951 426237 409157 029486 504634 758710 955121 638443 961536 708945 244130 921113 403999 060811 374319 308424 [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.