MinT - Information on Result #671951

Information on Result #671951

Linear OA(27¹⁵, 19737, F₂₇, 5) (dual of [19737, 19722, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 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, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27⁰, 731, F₂₇, 0) (dual of [731, 731, 1]-code) (see above)
linear OA(27¹, 731, F₂₇, 1) (dual of [731, 730, 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, 731, F₂₇, 1) (dual of [731, 730, 2]-code) (see above)
linear OA(27¹, 731, F₂₇, 1) (dual of [731, 730, 2]-code) (see above)
linear OA(27³, 731, F₂₇, 2) (dual of [731, 728, 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, 731, F₂₇, 5) (dual of [731, 722, 6]-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OA(27⁷, 703, F₂₇, 5) (dual of [703, 696, 6]-code), using
    - a code by Danev and Olsson [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.