MinT - Information on Result #658917

Information on Result #658917

Linear OA(8⁷⁵, 94, F₈, 45) (dual of [94, 19, 46]-code), using constructionÂ XX applied to AG(F,18P) âŠ‚ AG(F,30P) âŠ‚ AG(F,32P) based on

linear OA(8⁵⁷, 64, F₈, 45) (dual of [64, 7, 46]-code), using algebraic-geometric code AG(F,18P) 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]
linear OA(8⁴⁷, 64, F₈, 33) (dual of [64, 17, 34]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
linear OA(8⁴⁵, 64, F₈, 31) (dual of [64, 19, 32]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
linear OA(8¹⁵, 27, F₈, 11) (dual of [27, 12, 12]-code), using
- constructionÂ X applied to AG(F,6P) âŠ‚ AG(F,7P) [i] based on
  1. linear OA(8¹⁴, 24, F₈, 11) (dual of [24, 10, 12]-code), using algebraic-geometric code AG(F,6P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F₈ [i]
  2. linear OA(8¹², 24, F₈, 9) (dual of [24, 12, 10]-code), using algebraic-geometric code AG(F,7P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24 (see above)
  3. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹, 8, F₈, 1) (dual of [8, 7, 2]-code), using
  - Reedâ€“Solomon code RS(7,8) [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.