MinT - Information on Result #2622258

Information on Result #2622258

Linear OOA(3¹²⁷, 53, F₃, 3, 72) (dual of [(53, 3), 32, 73]-NRT-code), using strength reduction based on linear OOA(3¹²⁷, 53, F₃, 3, 73) (dual of [(53, 3), 32, 74]-NRT-code), using

constructionÂ X applied to AG(3;F,67P) âŠ‚ AG(3;F,76P) [i] based on
1. linear OOA(3¹¹⁸, 47, F₃, 3, 73) (dual of [(47, 3), 23, 74]-NRT-code), using algebraic-geometric NRT-code AG(3;F,67P) [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(3¹⁰⁹, 47, F₃, 3, 64) (dual of [(47, 3), 32, 65]-NRT-code), using algebraic-geometric NRT-code AG(3;F,76P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁹, 6, F₃, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁹, 7, F₃, 3, 8) (dual of [(7, 3), 12, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, 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.