MinT - Information on Result #1821746

Information on Result #1821746

OA(8¹¹², 580, S₈, 38), using trace code based on OA(64⁵⁶, 290, S₆₄, 38), using

discarding parts of the base [i] based on linear OA(128⁴⁸, 290, F₁₂₈, 38) (dual of [290, 242, 39]-code), using
- constructionÂ X applied to AG(F,248P) âŠ‚ AG(F,250P) [i] based on
  1. linear OA(128⁴⁷, 287, F₁₂₈, 38) (dual of [287, 240, 39]-code), using algebraic-geometric code AG(F,248P) [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(128⁴⁵, 287, F₁₂₈, 36) (dual of [287, 242, 37]-code), using algebraic-geometric code AG(F,250P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
  3. linear OA(128¹, 3, F₁₂₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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(8¹¹³, 581, S₈, 38)	[i]		Code Embedding in Larger Space
2	OA(8¹¹⁴, 582, S₈, 38)	[i]
3	OA(8¹¹⁵, 583, S₈, 38)	[i]
4	OA(8¹¹⁶, 584, S₈, 38)	[i]
5	OA(8¹¹⁷, 585, S₈, 38)	[i]