MinT - Information on Result #2260528

Information on Result #2260528

Linear OA(2¹³⁸, 178, F₂, 46) (dual of [178, 40, 47]-code), using 3 times code embedding in larger space based on linear OA(2¹³⁵, 175, F₂, 46) (dual of [175, 40, 47]-code), using

1 times truncation [i] based on linear OA(2¹³⁶, 176, F₂, 47) (dual of [176, 40, 48]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16¹², 22, F₁₆, 11) (dual of [22, 10, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.