MinT - Information on Result #1846301

Information on Result #1846301

OA(128⁷², 521, S₁₂₈, 51), using discarding parts of the base based on linear OA(256⁶³, 521, F₂₅₆, 51) (dual of [521, 458, 52]-code), using

constructionÂ X applied to AG(F,460P) âŠ‚ AG(F,465P) [i] based on
1. linear OA(256⁵⁹, 512, F₂₅₆, 51) (dual of [512, 453, 52]-code), using algebraic-geometric code AG(F,460P) [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(256⁵⁴, 512, F₂₅₆, 46) (dual of [512, 458, 47]-code), using algebraic-geometric code AG(F,465P) [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513 (see above)
3. linear OA(256⁴, 9, F₂₅₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,256)), using
  - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
    - Reedâ€“Solomon code RS(252,256) [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(128⁷³, 522, S₁₂₈, 51)	[i]		Code Embedding in Larger Space
2	OA(128⁷⁴, 523, S₁₂₈, 51)	[i]		Code Embedding in Larger Space