MinT - Information on Result #2180371

Information on Result #2180371

Linear OA(2¹⁵⁶, 192, F₂, 58) (dual of [192, 36, 59]-code), using strength reduction 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(2¹⁵⁵, 191, F₂, 57) (dual of [191, 36, 58]-code)	[i]		Truncation
2	Linear OA(2¹⁵⁴, 190, F₂, 56) (dual of [190, 36, 57]-code)	[i]		Truncation
3	Linear OOA(2¹⁵⁶, 96, F₂, 2, 58) (dual of [(96, 2), 36, 59]-NRT-code)	[i]		OOA Folding
4	Linear OOA(2¹⁵⁶, 64, F₂, 3, 58) (dual of [(64, 3), 36, 59]-NRT-code)	[i]		OOA Folding