MinT - Information on Result #2223672

Information on Result #2223672

Linear OA(2¹⁵⁴, 190, F₂, 57) (dual of [190, 36, 58]-code), using 2 times truncation based on linear OA(2¹⁵⁶, 192, F₂, 59) (dual of [192, 36, 60]-code), using

concatenation of two codes [i] based on
1. 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 OA(2¹⁵⁷, 193, F₂, 57) (dual of [193, 36, 58]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2¹⁵⁸, 194, F₂, 57) (dual of [194, 36, 58]-code)	[i]
3	Linear OA(2¹⁵⁹, 195, F₂, 57) (dual of [195, 36, 58]-code)	[i]
4	Linear OA(2¹⁶⁰, 196, F₂, 57) (dual of [196, 36, 58]-code)	[i]
5	Linear OA(2¹⁶¹, 197, F₂, 57) (dual of [197, 36, 58]-code)	[i]
6	Linear OA(2¹⁶², 198, F₂, 57) (dual of [198, 36, 58]-code)	[i]
7	Linear OA(2¹⁶³, 199, F₂, 57) (dual of [199, 36, 58]-code)	[i]
8	Linear OA(2¹⁶⁴, 200, F₂, 57) (dual of [200, 36, 58]-code)	[i]
9	Linear OA(2¹⁶⁵, 201, F₂, 57) (dual of [201, 36, 58]-code)	[i]
10	Linear OOA(2¹⁵⁴, 95, F₂, 2, 57) (dual of [(95, 2), 36, 58]-NRT-code)	[i]		OOA Folding
11	Linear OOA(2¹⁵⁴, 63, F₂, 3, 57) (dual of [(63, 3), 35, 58]-NRT-code)	[i]		OOA Folding