MinT - Information on Result #666492

Information on Result #666492

Linear OA(27¹⁵, 19710, F₂₇, 5) (dual of [19710, 19695, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 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, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27⁰, 730, F₂₇, 0) (dual of [730, 730, 1]-code) (see above)
linear OA(27¹, 730, F₂₇, 1) (dual of [730, 729, 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, 730, F₂₇, 1) (dual of [730, 729, 2]-code) (see above)
linear OA(27¹, 730, F₂₇, 1) (dual of [730, 729, 2]-code) (see above)
linear OA(27³, 730, F₂₇, 2) (dual of [730, 727, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
  - Hamming code H(3,27) [i]
linear OA(27⁹, 730, F₂₇, 5) (dual of [730, 721, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 730Â | 27⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (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.