MinT - Information on Result #1303681

Information on Result #1303681

Linear OA(16⁶³, 652, F₁₆, 27) (dual of [652, 589, 28]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(16⁶², 650, F₁₆, 27) (dual of [650, 588, 28]-code), using
- trace code [i] based on linear OA(256³¹, 325, F₂₅₆, 27) (dual of [325, 294, 28]-code), using
  - constructionÂ X applied to AG(F,292P) âŠ‚ AG(F,295P) [i] based on
    1. linear OA(256²⁹, 320, F₂₅₆, 27) (dual of [320, 291, 28]-code), using algebraic-geometric code AG(F,292P) [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(256²⁶, 320, F₂₅₆, 24) (dual of [320, 294, 25]-code), using algebraic-geometric code AG(F,295P) [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]
linear OA(16⁶², 651, F₁₆, 26) (dual of [651, 589, 27]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16⁶²Â > V_b^sâˆ’1(kâˆ’1)Â = 215 088332 340518 373670 892898 496421 190733 399248 366357 064330 490104 198789 980376 [i]
linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [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(16⁶³, 645, F₁₆, 2, 27) (dual of [(645, 2), 1227, 28]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (36, 63, 645)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound