MinT - Information on Result #2223540

Information on Result #2223540

Linear OA(2¹⁴³, 183, F₂, 48) (dual of [183, 40, 49]-code), using 1 times truncation based on linear OA(2¹⁴⁴, 184, F₂, 49) (dual of [184, 40, 50]-code), using

strength reduction [i] based on linear OA(2¹⁴⁴, 184, F₂, 51) (dual of [184, 40, 52]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16¹³, 23, F₁₆, 12) (dual of [23, 10, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹³, 24, F₁₆, 12) (dual of [24, 11, 13]-code), using
      - extended algebraic-geometric code AG_e(F,11P) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁴³, 61, F₂, 3, 48) (dual of [(61, 3), 40, 49]-NRT-code)	[i]		OOA Folding