MinT - Information on Result #1297324

Information on Result #1297324

Linear OA(2¹⁷⁷, 210, F₂, 66) (dual of [210, 33, 67]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2¹⁶⁷, 199, F₂, 66) (dual of [199, 32, 67]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶⁸, 200, F₂, 67) (dual of [200, 32, 68]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹⁷, 25, F₁₆, 16) (dual of [25, 8, 17]-code), using
      - extended algebraic-geometric code AG_e(F,8P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 25, using
        sharp bound on the number of rational points on curves with genus 1 [i]
    2. linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
      - Reedâ€“Muller code RM(1,3) [i]
      - caps in base bÂ =Â 2 [i]
linear OA(2¹⁶⁷, 200, F₂, 56) (dual of [200, 33, 57]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2¹⁶⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 89 366223 488551 309908 066340 050493 995901 127276 302208 [i]
linear OA(2⁹, 10, F₂, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,2)), using
- dual of repetition code with length 10 [i]

Mode: Linear.

None.

None.