MinT - Information on Result #1018627

Information on Result #1018627

Linear OOA(81⁷⁶, 5592584, F₈₁, 3, 12) (dual of [(5592584, 3), 16777676, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81²⁴, 2796283, F₈₁, 3, 6) (dual of [(2796283, 3), 8388825, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81³, 82, F₈₁, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;243,81) [i]
  2. linear OOA(81²¹, 2796201, F₈₁, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(81⁵², 2796301, F₈₁, 3, 12) (dual of [(2796301, 3), 8388851, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁷, 100, F₈₁, 3, 6) (dual of [(100, 3), 293, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,293P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(81⁴⁵, 2796201, F₈₁, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’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.