MinT - Information on Result #670029

Information on Result #670029

Linear OA(81²⁹, 6642, F₈₁, 11) (dual of [6642, 6613, 12]-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(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(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code) (see above)
linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code) (see above)
linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code) (see above)
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(81², 82, F₈₁, 2) (dual of [82, 80, 3]-code or 82-arc in PG(1,81)) (see above)
linear OA(81³, 82, F₈₁, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), using
- extended Reedâ€“Solomon code RS_e(79,81) [i]
- oval in PG(2,Â 81) [i]
linear OA(81⁵, 82, F₈₁, 5) (dual of [82, 77, 6]-code or 82-arc in PG(4,81)), using
- extended Reedâ€“Solomon code RS_e(77,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82Â | 81²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OA(81¹¹, 82, F₈₁, 11) (dual of [82, 71, 12]-code or 82-arc in PG(10,81)), using
- extended Reedâ€“Solomon code RS_e(71,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82Â | 81²âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.