MinT - Information on Result #1296991

Information on Result #1296991

Linear OA(16⁸⁶, 654, F₁₆, 38) (dual of [654, 568, 39]-code), using trace code based on linear OA(256⁴³, 327, F₂₅₆, 38) (dual of [327, 284, 39]-code), using

constructionÂ X applied to AG(F,281P) âŠ‚ AG(F,285P) [i] based on
1. linear OA(256⁴⁰, 320, F₂₅₆, 38) (dual of [320, 280, 39]-code), using algebraic-geometric code AG(F,281P) [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(256³⁶, 320, F₂₅₆, 34) (dual of [320, 284, 35]-code), using algebraic-geometric code AG(F,285P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
3. linear OA(256³, 7, F₂₅₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,256) or 7-cap in PG(2,256)), using
  - discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
    - Reedâ€“Solomon code RS(253,256) [i]

Mode: Linear.

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	Linear OOA(16⁸⁶, 646, F₁₆, 2, 38) (dual of [(646, 2), 1206, 39]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (48, 86, 646)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound