MinT - Information on Result #1019249

Information on Result #1019249

Linear OOA(128⁷⁶, 5592681, F₁₂₈, 3, 12) (dual of [(5592681, 3), 16777967, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128²⁴, 2796330, F₁₂₈, 3, 6) (dual of [(2796330, 3), 8388966, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128³, 129, F₁₂₈, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;384,128) [i]
  2. linear OOA(128²¹, 2796201, F₁₂₈, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128²¹, large, F₁₂₈, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(128⁵², 2796351, F₁₂₈, 3, 12) (dual of [(2796351, 3), 8389001, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁷, 150, F₁₂₈, 3, 6) (dual of [(150, 3), 443, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,443P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(128⁴⁵, 2796201, F₁₂₈, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128⁴⁵, large, F₁₂₈, 12) (dual of [large, large−45, 13]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’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.