MinT - Information on Result #948707

Information on Result #948707

Linear OOA(2¹³⁰, 54, F₂, 3, 47) (dual of [(54, 3), 32, 48]-NRT-code), using OOA 3-folding based on linear OA(2¹³⁰, 162, F₂, 47) (dual of [162, 32, 48]-code), using

2 times code embedding in larger space [i] based on linear OA(2¹²⁸, 160, F₂, 47) (dual of [160, 32, 48]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16¹², 20, F₁₆, 11) (dual of [20, 8, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹², 24, F₁₆, 11) (dual of [24, 12, 12]-code), using
      - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
    - Reedâ€“Muller code RM(1,3) [i]
    - caps in base bÂ =Â 2 [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.