MinT - Information on Result #666487

Information on Result #666487

Linear OA(27¹⁷, 766, F₂₇, 7) (dual of [766, 749, 8]-code), using generalized (u,Â u+v)-construction based on

linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code) (see above)
linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code) (see above)
linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code) (see above)
linear OA(27², 28, F₂₇, 2) (dual of [28, 26, 3]-code or 28-arc in PG(1,27)), using
- extended Reedâ€“Solomon code RS_e(26,27) [i]
- Hamming code H(2,27) [i]
linear OA(27³, 28, F₂₇, 3) (dual of [28, 25, 4]-code or 28-arc in PG(2,27) or 28-cap in PG(2,27)), using
- extended Reedâ€“Solomon code RS_e(25,27) [i]
- oval in PG(2,Â 27) [i]
linear OA(27⁸, 38, F₂₇, 7) (dual of [38, 30, 8]-code), using
- extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, 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.