MinT - Information on Result #1297105

Information on Result #1297105

Linear OA(256⁶⁰, 644, F₂₅₆, 37) (dual of [644, 584, 38]-code), using (u,Â u+v)-construction based on

linear OA(256²⁰, 321, F₂₅₆, 18) (dual of [321, 301, 19]-code), using
- extended algebraic-geometric code AG_e(F,302P) [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]
linear OA(256⁴⁰, 323, F₂₅₆, 37) (dual of [323, 283, 38]-code), using
- constructionÂ X applied to AG(F,282P) âŠ‚ AG(F,284P) [i] based on
  1. linear OA(256³⁹, 320, F₂₅₆, 37) (dual of [320, 281, 38]-code), using algebraic-geometric code AG(F,282P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
  2. linear OA(256³⁷, 320, F₂₅₆, 35) (dual of [320, 283, 36]-code), using algebraic-geometric code AG(F,284P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
  3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(256⁶⁰, 611, F₂₅₆, 2, 37) (dual of [(611, 2), 1162, 38]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound