MinT - Information on Result #2770929

Information on Result #2770929

Linear OOA(3¹⁴⁴, 57, F₃, 4, 77) (dual of [(57, 4), 84, 78]-NRT-code), using strength reduction based on linear OOA(3¹⁴⁴, 57, F₃, 4, 78) (dual of [(57, 4), 84, 79]-NRT-code), using

constructionÂ X applied to AG(4;F,109P) âŠ‚ AG(4;F,128P) [i] based on
1. linear OOA(3¹²³, 47, F₃, 4, 78) (dual of [(47, 4), 65, 79]-NRT-code), using algebraic-geometric NRT-code AG(4;F,109P) [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(3¹⁰⁴, 47, F₃, 4, 59) (dual of [(47, 4), 84, 60]-NRT-code), using algebraic-geometric NRT-code AG(4;F,128P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3²¹, 10, F₃, 4, 18) (dual of [(10, 4), 19, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,21P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, 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.