MinT - Information on Result #907032

Information on Result #907032

Linear OOA(81¹⁸, 6678, F₈₁, 2, 7) (dual of [(6678, 2), 13338, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] 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 OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
linear OOA(81⁴, 100, F₈₁, 2, 3) (dual of [(100, 2), 196, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁴, 6562, F₈₁, 2, 3) (dual of [(6562, 2), 13120, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁴, 6562, F₈₁, 3) (dual of [6562, 6558, 4]-code or 6562-cap in PG(3,81)), using
    - ovoid in PG(3,Â 81) [i]
linear OOA(81⁸, 100, F₈₁, 2, 7) (dual of [(100, 2), 192, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,192P) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁷⁵, 4200979, F₈₁, 2, 15) (dual of [(4200979, 2), 8401883, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁷¹, 4200979, F₈₁, 2, 14) (dual of [(4200979, 2), 8401887, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs