MinT - Information on Result #2282224

Information on Result #2282224

Linear OA(8¹⁷¹, 1039, F₈, 54) (dual of [1039, 868, 55]-code), using 1 times code embedding in larger space based on linear OA(8¹⁷⁰, 1038, F₈, 54) (dual of [1038, 868, 55]-code), using

trace code [i] based on linear OA(64⁸⁵, 519, F₆₄, 54) (dual of [519, 434, 55]-code), using
- constructionÂ X applied to AG(F,457P) âŠ‚ AG(F,461P) [i] based on
  1. linear OA(64⁸², 512, F₆₄, 54) (dual of [512, 430, 55]-code), using algebraic-geometric code AG(F,457P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]
  2. linear OA(64⁷⁸, 512, F₆₄, 50) (dual of [512, 434, 51]-code), using algebraic-geometric code AG(F,461P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OA(64³, 7, F₆₄, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
    - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
      - Reedâ€“Solomon code RS(61,64) [i]

Mode: Constructive and 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.

Other Results with Identical Parameters

None.

Depending Results

None.