MinT - Information on Result #2528871

Information on Result #2528871

Linear OOA(2⁹⁶, 72, F₂, 2, 36) (dual of [(72, 2), 48, 37]-NRT-code), using strength reduction based on linear OOA(2⁹⁶, 72, F₂, 2, 37) (dual of [(72, 2), 48, 38]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²⁰, 18, F₈, 2, 18) (dual of [(18, 2), 16, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 18, using
    - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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.

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.