MinT - Information on Result #2225059

Information on Result #2225059

Linear OA(2¹⁷⁹, 231, F₂, 58) (dual of [231, 52, 59]-code), using 1 times truncation based on linear OA(2¹⁸⁰, 232, F₂, 59) (dual of [232, 52, 60]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁶, 29, F₁₆, 14) (dual of [29, 13, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁶, 33, F₁₆, 14) (dual of [33, 17, 15]-code), using
    - extended algebraic-geometric code AG_e(F,18P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, 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(2¹⁸¹, 233, F₂, 58) (dual of [233, 52, 59]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(2¹⁷⁹, 115, F₂, 2, 58) (dual of [(115, 2), 51, 59]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹⁷⁹, 77, F₂, 3, 58) (dual of [(77, 3), 52, 59]-NRT-code)	[i]	OOA Folding