MinT - Information on Result #2774710

Information on Result #2774710

Linear OOA(3²¹⁰, 68, F₃, 4, 116) (dual of [(68, 4), 62, 117]-NRT-code), using strength reduction based on linear OOA(3²¹⁰, 68, F₃, 4, 117) (dual of [(68, 4), 62, 118]-NRT-code), using

constructionÂ X applied to AG(4;F,70P) âŠ‚ AG(4;F,106P) [i] based on
1. linear OOA(3¹⁶², 47, F₃, 4, 117) (dual of [(47, 4), 26, 118]-NRT-code), using algebraic-geometric NRT-code AG(4;F,70P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹²⁶, 47, F₃, 4, 81) (dual of [(47, 4), 62, 82]-NRT-code), using algebraic-geometric NRT-code AG(4;F,106P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁴⁸, 21, F₃, 4, 35) (dual of [(21, 4), 36, 36]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁴⁸, 24, F₃, 4, 35) (dual of [(24, 4), 48, 36]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,60P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [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.