MinT - Information on Result #1846122

Information on Result #1846122

OA(128⁵⁶, 523, S₁₂₈, 36), using discarding parts of the base based on linear OA(256⁴⁹, 523, F₂₅₆, 36) (dual of [523, 474, 37]-code), using

constructionÂ X applied to AG(F,475P) âŠ‚ AG(F,481P) [i] based on
1. linear OA(256⁴⁴, 512, F₂₅₆, 36) (dual of [512, 468, 37]-code), using algebraic-geometric code AG(F,475P) [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
  - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]
2. linear OA(256³⁸, 512, F₂₅₆, 30) (dual of [512, 474, 31]-code), using algebraic-geometric code AG(F,481P) [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513 (see above)
3. linear OA(256⁵, 11, F₂₅₆, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,256)), using
  - discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
    - Reedâ€“Solomon code RS(251,256) [i]

Mode: Arbitrary.

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(128⁵⁷, 524, S₁₂₈, 36)	[i]		Code Embedding in Larger Space
2	OA(128⁵⁸, 525, S₁₂₈, 36)	[i]		Code Embedding in Larger Space