MinT - Information on Result #1014698

Information on Result #1014698

Linear OOA(8¹⁷⁰, 5603338, F₈, 3, 17) (dual of [(5603338, 3), 16809844, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁴⁰, 10936, F₈, 3, 8) (dual of [(10936, 3), 32768, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁵, 14, F₈, 3, 4) (dual of [(14, 3), 37, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,37P) [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]
  2. linear OOA(8³⁵, 10922, F₈, 3, 8) (dual of [(10922, 3), 32731, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8³⁵, 32766, F₈, 8) (dual of [32766, 32731, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(8³⁵, 32767, F₈, 8) (dual of [32767, 32732, 9]-code), using
        1 times truncation [i] based on linear OA(8³⁶, 32768, F₈, 9) (dual of [32768, 32732, 10]-code), using
        an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(8¹³⁰, 5592402, F₈, 3, 17) (dual of [(5592402, 3), 16777076, 18]-NRT-code), using
- trace code [i] based on linear OOA(64⁶⁵, 2796201, F₆₄, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.