MinT - Information on Result #1020056

Information on Result #1020056

Linear OOA(256⁶³, 5592917, F₂₅₆, 3, 13) (dual of [(5592917, 3), 16778688, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁹, 2796458, F₂₅₆, 3, 6) (dual of [(2796458, 3), 8389355, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256³, 257, F₂₅₆, 3, 3) (dual of [(257, 3), 768, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;768,256) [i]
  2. linear OOA(256¹⁶, 2796201, F₂₅₆, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(256⁴⁴, 2796459, F₂₅₆, 3, 13) (dual of [(2796459, 3), 8389333, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁷, 258, F₂₅₆, 3, 6) (dual of [(258, 3), 767, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256³⁷, 2796201, F₂₅₆, 3, 13) (dual of [(2796201, 3), 8388566, 14]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.