MinT - Information on Result #641431

Information on Result #641431

Linear OA(8¹²⁸, 133, F₈, 103) (dual of [133, 5, 104]-code), using juxtaposition based on

linear OA(8⁵⁶, 61, F₈, 47) (dual of [61, 5, 48]-code), using
- 4 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(8⁶⁷, 72, F₈, 55) (dual of [72, 5, 56]-code), using
- constructionÂ X applied to C([0,27]) âŠ‚ C([1,27]) [i] based on
  1. linear OA(8⁶¹, 65, F₈, 55) (dual of [65, 4, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 65Â | 8⁴âˆ’1, defining interval IÂ =Â [0,27], and minimum distance dÂ â‰¥ |{−27,−26,…,27}|+1Â =Â 56 (BCH-bound) [i]
  2. linear OA(8⁶⁰, 65, F₈, 48) (dual of [65, 5, 49]-code), using the narrow-sense BCH-code C(I) with length 65Â | 8⁴âˆ’1, defining interval IÂ =Â [1,27], and minimum distance dÂ â‰¥ |{−8,20,48,…,8}|+1Â =Â 49 (BCH-bound) [i]
  3. linear OA(8⁶, 7, F₈, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,8)), using
    - dual of repetition code with length 7 [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.