MinT - Information on Result #1013193

Information on Result #1013193

Linear OOA(5¹²⁶, 4194360, F₅, 3, 12) (dual of [(4194360, 3), 12582954, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁴, 59, F₅, 3, 6) (dual of [(59, 3), 163, 7]-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(5¹⁰, 33, F₅, 3, 6) (dual of [(33, 3), 89, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 33)-net over F₅, using
      - linear code embedding found in a computer search [i]
linear OOA(5¹¹², 4194301, F₅, 3, 12) (dual of [(4194301, 3), 12582791, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(5¹¹², 8388602, F₅, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
  - trace code [i] based on linear OOA(25⁵⁶, 4194301, F₂₅, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁵⁶, 8388602, F₂₅, 12) (dual of [8388602, 8388546, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’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.