MinT - Information on Result #1117310

Information on Result #1117310

Linear OOA(3²³², 5592413, F₃, 5, 12) (dual of [(5592413, 5), 27961833, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶³, 2796205, F₃, 5, 6) (dual of [(2796205, 5), 13980962, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3³, 4, F₃, 5, 3) (dual of [(4, 5), 17, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;17,3) [i]
  2. linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(3¹⁶⁹, 2796208, F₃, 5, 12) (dual of [(2796208, 5), 13980871, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁷, 7, F₃, 5, 6) (dual of [(7, 5), 28, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,28P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹⁶², 2796201, F₃, 5, 12) (dual of [(2796201, 5), 13980843, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(3¹⁶², 5592402, F₃, 3, 12) (dual of [(5592402, 3), 16777044, 13]-NRT-code), using
      - trace code [i] based on linear OOA(9⁸¹, 2796201, F₉, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
        OOA 3-folding [i] based on linear OA(9⁸¹, large, F₉, 12) (dual of [large, large−81, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.