MinT - Information on Result #2223472

Information on Result #2223472

Linear OA(2¹⁵¹, 183, F₂, 57) (dual of [183, 32, 58]-code), using 1 times truncation based on linear OA(2¹⁵², 184, F₂, 58) (dual of [184, 32, 59]-code), using

strength reduction [i] based on linear OA(2¹⁵², 184, F₂, 59) (dual of [184, 32, 60]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16¹⁵, 23, F₁₆, 14) (dual of [23, 8, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹⁵, 24, F₁₆, 14) (dual of [24, 9, 15]-code), using
      - extended algebraic-geometric code AG_e(F,9P) [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(2¹⁵¹, 61, F₂, 3, 57) (dual of [(61, 3), 32, 58]-NRT-code)	[i]		OOA Folding