MinT - Information on Result #670048

Information on Result #670048

Linear OA(81⁹, 6660, F₈₁, 4) (dual of [6660, 6651, 5]-code), using generalized (u,Â u+v)-construction based on

linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code) (see above)
linear OA(81², 82, F₈₁, 2) (dual of [82, 80, 3]-code or 82-arc in PG(1,81)), using
- extended Reedâ€“Solomon code RS_e(80,81) [i]
- Hamming code H(2,81) [i]
linear OA(81⁵, 100, F₈₁, 4) (dual of [100, 95, 5]-code), using
- extended algebraic-geometric code AG_e(F,95P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
  - a function field by SÃ©mirat [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.