MinT - Information on Result #2223394

Information on Result #2223394

Linear OA(2¹⁵⁰, 182, F₂, 57) (dual of [182, 32, 58]-code), using 2 times truncation 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		Method
1	Linear OA(2¹⁵³, 185, F₂, 57) (dual of [185, 32, 58]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(2¹⁵⁰, 91, F₂, 2, 57) (dual of [(91, 2), 32, 58]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹⁵⁰, 60, F₂, 3, 57) (dual of [(60, 3), 30, 58]-NRT-code)	[i]	OOA Folding