MinT - Information on Result #1845894

Information on Result #1845894

OA(128³², 329, S₁₂₈, 22), using discarding parts of the base based on linear OA(256²⁸, 329, F₂₅₆, 22) (dual of [329, 301, 23]-code), using

constructionÂ X applied to AG(F,297P) âŠ‚ AG(F,302P) [i] based on
1. linear OA(256²⁴, 320, F₂₅₆, 22) (dual of [320, 296, 23]-code), using algebraic-geometric code AG(F,297P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
  - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OA(256¹⁹, 320, F₂₅₆, 17) (dual of [320, 301, 18]-code), using algebraic-geometric code AG(F,302P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (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(128³³, 330, S₁₂₈, 22)	[i]		Code Embedding in Larger Space
2	OA(128³⁴, 331, S₁₂₈, 22)	[i]		Code Embedding in Larger Space