MinT - Information on Result #1296992

Information on Result #1296992

Linear OA(16⁸⁶, 650, F₁₆, 39) (dual of [650, 564, 40]-code), using trace code based on linear OA(256⁴³, 325, F₂₅₆, 39) (dual of [325, 282, 40]-code), using

constructionÂ X applied to AG(F,280P) âŠ‚ AG(F,283P) [i] based on
1. linear OA(256⁴¹, 320, F₂₅₆, 39) (dual of [320, 279, 40]-code), using algebraic-geometric code AG(F,280P) [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(256³⁸, 320, F₂₅₆, 36) (dual of [320, 282, 37]-code), using algebraic-geometric code AG(F,283P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
3. linear OA(256², 5, F₂₅₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
  - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
    - Reedâ€“Solomon code RS(254,256) [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, 553, F₁₆, 2, 39) (dual of [(553, 2), 1020, 40]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound