MinT - Information on Result #1020017

Information on Result #1020017

Linear OOA(256⁶², 5592920, F₂₅₆, 3, 12) (dual of [(5592920, 3), 16778698, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256²⁰, 2861738, F₂₅₆, 3, 6) (dual of [(2861738, 3), 8585194, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 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(256⁴², 2796460, F₂₅₆, 3, 12) (dual of [(2796460, 3), 8389338, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁸, 259, F₂₅₆, 3, 6) (dual of [(259, 3), 769, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 8, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256³⁴, 2796201, F₂₅₆, 3, 12) (dual of [(2796201, 3), 8388569, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’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.