MinT - Information on Result #2610304

Information on Result #2610304

Linear OOA(2⁶⁸, 25, F₂, 3, 42) (dual of [(25, 3), 7, 43]-NRT-code), using strength reduction based on linear OOA(2⁶⁸, 25, F₂, 3, 43) (dual of [(25, 3), 7, 44]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁴, 7, F₂, 3, 11) (dual of [(7, 3), 7, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2⁴⁷, 18, F₂, 3, 31) (dual of [(18, 3), 7, 32]-NRT-code), using
  - repeating each code word 2 times [i] based on linear OOA(2²⁰, 9, F₂, 3, 15) (dual of [(9, 3), 7, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,11P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
      - an explicitly constructive algebraic function field [i]

Mode: Constructive and 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.