MinT - Information on Result #1297178

Information on Result #1297178

Linear OA(256²⁵, 546, F₂₅₆, 16) (dual of [546, 521, 17]-code), using (u,Â u+v)-construction based on

linear OA(256⁸, 257, F₂₅₆, 8) (dual of [257, 249, 9]-code or 257-arc in PG(7,256)), using
- extended Reedâ€“Solomon code RS_e(249,256) [i]
- algebraic-geometric code AG(F,124P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
- algebraic-geometric code AG(F, Q+82P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+49P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
linear OA(256¹⁷, 289, F₂₅₆, 16) (dual of [289, 272, 17]-code), using
- extended algebraic-geometric code AG_e(F,272P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
  - sharp bound on the number of rational points on curves with genus 1 [i]

Mode: Linear.

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