MinT - Information on Result #2535893

Information on Result #2535893

Linear OOA(2²¹⁸, 123, F₂, 2, 102) (dual of [(123, 2), 28, 103]-NRT-code), using 4 step truncation based on linear OOA(2²²², 125, F₂, 2, 106) (dual of [(125, 2), 28, 107]-NRT-code), using

strength reduction [i] based on linear OOA(2²²², 125, F₂, 2, 107) (dual of [(125, 2), 28, 108]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹⁸, 25, F₁₆, 17) (dual of [25, 7, 18]-code), using
    - extended algebraic-geometric code AG_e(F,7P) [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 OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [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

None.