MinT - Information on Result #661614

Information on Result #661614

Linear OA(8¹²⁸, 133, F₈, 105) (dual of [133, 5, 106]-code), using juxtaposition based on

linear OA(8⁵⁸, 63, F₈, 49) (dual of [63, 5, 50]-code), using
- 2 times truncation [i] based on 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]
linear OA(8⁶⁵, 70, F₈, 55) (dual of [70, 5, 56]-code), using
- constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,13P) [i] based on
  1. 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 (see above)
  2. linear OA(8⁵⁹, 64, F₈, 50) (dual of [64, 5, 51]-code) (see above)
  3. 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(8¹²⁸, 133, F₈, 104) (dual of [133, 5, 105]-code)	[i]		Strength Reduction