MinT - Information on Result #1300099

Information on Result #1300099

Linear OA(4¹¹⁸, 147, F₄, 62) (dual of [147, 29, 63]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹¹⁷, 145, F₄, 62) (dual of [145, 28, 63]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(4¹¹⁶, 143, F₄, 62) (dual of [143, 27, 63]-code), using
    - 1 times truncation [i] based on linear OA(4¹¹⁷, 144, F₄, 63) (dual of [144, 27, 64]-code), using
      - concatenation of two codes [i] based on
        linear OA(64¹⁵, 24, F₆₄, 15) (dual of [24, 9, 16]-code or 24-arc in PG(14,64)), using
        discarding factors / shortening the dual code based on linear OA(64¹⁵, 64, F₆₄, 15) (dual of [64, 49, 16]-code or 64-arc in PG(14,64)), using
        Reedâ€“Solomon code RS(49,64) [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(4¹¹⁶, 144, F₄, 61) (dual of [144, 28, 62]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹¹⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 6514 586982 402678 887179 272854 761194 821427 507839 517562 119399 256298 625256 [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(4¹¹⁷, 146, F₄, 61) (dual of [146, 29, 62]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹¹⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 18917 008385 882492 128301 504144 997212 444359 875836 467697 061575 875387 295296 [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.