MinT - Information on Result #2872303

Information on Result #2872303

Linear OOA(2²²⁶, 51, F₂, 5, 148) (dual of [(51, 5), 29, 149]-NRT-code), using 2¹ times duplication based on linear OOA(2²²⁵, 51, F₂, 5, 148) (dual of [(51, 5), 30, 149]-NRT-code), using

strength reduction [i] based on linear OOA(2²²⁵, 51, F₂, 5, 149) (dual of [(51, 5), 30, 150]-NRT-code), using
- constructionÂ X applied to AG(5;F,45P) âŠ‚ AG(5;F,49P) [i] based on
  1. linear OOA(2²¹⁸, 48, F₂, 5, 149) (dual of [(48, 5), 22, 150]-NRT-code), using algebraic-geometric NRT-code AG(5;F,45P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
  2. linear OOA(2²¹⁰, 48, F₂, 5, 141) (dual of [(48, 5), 30, 142]-NRT-code), using algebraic-geometric NRT-code AG(5;F,49P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
  3. linear OOA(2⁷, 3, F₂, 5, 7) (dual of [(3, 5), 8, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;8,2) [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.