MinT - Information on Result #1821901

Information on Result #1821901

OA(8¹⁵⁴, 584, S₈, 55), using trace code based on OA(64⁷⁷, 292, S₆₄, 55), using

discarding parts of the base [i] based on linear OA(128⁶⁶, 292, F₁₂₈, 55) (dual of [292, 226, 56]-code), using
- constructionÂ X applied to AG(F,231P) âŠ‚ AG(F,234P) [i] based on
  1. linear OA(128⁶⁴, 287, F₁₂₈, 55) (dual of [287, 223, 56]-code), using algebraic-geometric code AG(F,231P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]
  2. linear OA(128⁶¹, 287, F₁₂₈, 52) (dual of [287, 226, 53]-code), using algebraic-geometric code AG(F,234P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
  3. linear OA(128², 5, F₁₂₈, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,128)), using
    - discarding factors / shortening the dual code based on linear OA(128², 128, F₁₂₈, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
      - Reedâ€“Solomon code RS(126,128) [i]

Mode: Constructive.

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	OA(8¹⁵⁵, 585, S₈, 55)	[i]		Code Embedding in Larger Space
2	OA(8¹⁵⁶, 586, S₈, 55)	[i]
3	OA(8¹⁵⁷, 587, S₈, 55)	[i]
4	OA(8¹⁵⁸, 588, S₈, 55)	[i]
5	OA(8¹⁵⁹, 589, S₈, 55)	[i]