MinT - Information on Result #2851679

Information on Result #2851679

Linear OOA(3¹³⁶, 53, F₃, 5, 75) (dual of [(53, 5), 129, 76]-NRT-code), using strength reduction based on linear OOA(3¹³⁶, 53, F₃, 5, 76) (dual of [(53, 5), 129, 77]-NRT-code), using

constructionÂ X applied to AG(5;F,158P) âŠ‚ AG(5;F,173P) [i] based on
1. linear OOA(3¹²¹, 47, F₃, 5, 76) (dual of [(47, 5), 114, 77]-NRT-code), using algebraic-geometric NRT-code AG(5;F,158P) [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(3¹⁰⁶, 47, F₃, 5, 61) (dual of [(47, 5), 129, 62]-NRT-code), using algebraic-geometric NRT-code AG(5;F,173P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3¹⁵, 6, F₃, 5, 14) (dual of [(6, 5), 15, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁵, 7, F₃, 5, 14) (dual of [(7, 5), 20, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,20P) [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.