MinT - Information on Result #1188252

Information on Result #1188252

Digital (48, 55, 2796226)-net over F₅, using net defined by OOA based on linear OOA(5⁵⁵, 2796226, F₅, 9, 7) (dual of [(2796226, 9), 25165979, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(5⁵⁵, 2796227, F₅, 3, 7) (dual of [(2796227, 3), 8388626, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁴, 26, F₅, 3, 3) (dual of [(26, 3), 74, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5⁴, 26, F₅, 2, 3) (dual of [(26, 2), 48, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
  2. linear OOA(5⁵¹, 2796201, F₅, 3, 7) (dual of [(2796201, 3), 8388552, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5⁵¹, large, F₅, 7) (dual of [large, large−51, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.