MinT - Information on Result #1297304

Information on Result #1297304

Linear OA(2¹⁷⁰, 212, F₂, 58) (dual of [212, 42, 59]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2¹⁵⁹, 199, F₂, 58) (dual of [199, 40, 59]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶⁰, 200, F₂, 59) (dual of [200, 40, 60]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹⁵, 25, F₁₆, 14) (dual of [25, 10, 15]-code), using
      - extended algebraic-geometric code AG_e(F,10P) [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(2¹⁵⁹, 201, F₂, 51) (dual of [201, 42, 52]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2¹⁵⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 674353 227563 459664 641213 586620 598732 169971 625732 [i]
linear OA(2⁹, 11, F₂, 6) (dual of [11, 2, 7]-code), using
- 1 times truncation [i] based on linear OA(2¹⁰, 12, F₂, 7) (dual of [12, 2, 8]-code), using
  - repeating each code word 4 times [i] based on linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: Linear.

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