MinT - Information on Result #2223231

Information on Result #2223231

Linear OA(2¹³³, 189, F₂, 42) (dual of [189, 56, 43]-code), using 1 times truncation based on linear OA(2¹³⁴, 190, F₂, 43) (dual of [190, 56, 44]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁴, 38, F₁₆, 21) (dual of [38, 14, 22]-code), using
  - extended algebraic-geometric code AG_e(F,16P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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(2¹³⁵, 191, F₂, 42) (dual of [191, 56, 43]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹³⁶, 192, F₂, 42) (dual of [192, 56, 43]-code)	[i]	Code Embedding in Larger Space
3	Linear OOA(2¹³³, 94, F₂, 2, 42) (dual of [(94, 2), 55, 43]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2¹³³, 63, F₂, 3, 42) (dual of [(63, 3), 56, 43]-NRT-code)	[i]	OOA Folding