MinT - Information on Result #661598

Information on Result #661598

Linear OA(8⁸⁸, 93, F₈, 70) (dual of [93, 5, 71]-code), using juxtaposition based on

linear OA(8⁹, 14, F₈, 8) (dual of [14, 5, 9]-code), using
- extended algebraic-geometric code AG_e(F,5P) [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]
linear OA(8⁷⁴, 79, F₈, 61) (dual of [79, 5, 62]-code), using
- constructionÂ XX applied to AG(F,0P) âŠ‚ AG(F,10P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(8⁶³, 64, F₈, 63) (dual of [64, 1, 64]-code or 64-arc in PG(62,8)), using algebraic-geometric code AG(F,0P) [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 OA(8⁶¹, 64, F₈, 55) (dual of [64, 3, 56]-code), using algebraic-geometric code AG(F,10P) 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]
  3. linear OA(8⁵⁹, 64, F₈, 50) (dual of [64, 5, 51]-code), using algebraic-geometric code AG(F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  4. linear OA(8⁵, 9, F₈, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,8)), using
    - extended Reedâ€“Solomon code RS_e(4,8) [i]
  5. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)), using
    - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
      - Reedâ€“Solomon code RS(4,8) [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.