MinT - Information on Result #906764

Information on Result #906764

Linear OOA(27¹⁸, 776, F₂₇, 2, 7) (dual of [(776, 2), 1534, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] 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 OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
linear OOA(27², 28, F₂₇, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;54,27) [i]
linear OOA(27⁴, 38, F₂₇, 2, 3) (dual of [(38, 2), 72, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(27⁴, 730, F₂₇, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁴, 730, F₂₇, 3) (dual of [730, 726, 4]-code or 730-cap in PG(3,27)), using
    - ovoid in PG(3,Â 27) [i]
linear OOA(27⁸, 38, F₂₇, 2, 7) (dual of [(38, 2), 68, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,68P) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(27⁸⁹, 4195077, F₂₇, 2, 15) (dual of [(4195077, 2), 8390065, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(27⁸⁴, 4195077, F₂₇, 2, 14) (dual of [(4195077, 2), 8390070, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs