MinT - Information on Result #2450457

Information on Result #2450457

Linear OOA(8¹³⁸, 76, F₈, 2, 114) (dual of [(76, 2), 14, 115]-NRT-code), using strength reduction based on linear OOA(8¹³⁸, 76, F₈, 2, 115) (dual of [(76, 2), 14, 116]-NRT-code), using

constructionÂ X applied to AG(2;F,12P) âŠ‚ AG(2;F,26P) [i] based on
1. linear OOA(8¹²⁴, 64, F₈, 2, 115) (dual of [(64, 2), 4, 116]-NRT-code), using algebraic-geometric NRT-code AG(2;F,12P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]
2. linear OOA(8¹¹⁴, 64, F₈, 2, 101) (dual of [(64, 2), 14, 102]-NRT-code), using algebraic-geometric NRT-code AG(2;F,26P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁴, 12, F₈, 2, 13) (dual of [(12, 2), 10, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁴, 14, F₈, 2, 13) (dual of [(14, 2), 14, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,14P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [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.