MinT - Information on Result #671942

Information on Result #671942

Linear OA(8¹⁰², 107, F₈, 81) (dual of [107, 5, 82]-code), using juxtaposition based on

linear OA(8³⁷, 42, F₈, 29) (dual of [42, 5, 30]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)) (see above)
  3. linear OA(8⁵, 6, F₈, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,8)), using
    - dual of repetition code with length 6 [i]
  4. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)), using
    - complete OA / dual of code with only one code word [i]
  5. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)) (see above)
  6. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)) (see above)
  7. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)) (see above)
linear OA(8⁶⁰, 65, F₈, 51) (dual of [65, 5, 52]-code), using
- constructionÂ X applied to AG(F,12P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(8⁶⁰, 64, F₈, 51) (dual of [64, 4, 52]-code), using algebraic-geometric code AG(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 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)
  3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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.