MinT - Information on Result #1013175

Information on Result #1013175

Linear OOA(5¹⁴⁶, 5592456, F₅, 3, 12) (dual of [(5592456, 3), 16777222, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5⁴⁶, 2796267, F₅, 3, 6) (dual of [(2796267, 3), 8388755, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁵, 66, F₅, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
        caps completed using a computer search [i]
  2. linear OOA(5⁴¹, 2796201, F₅, 3, 6) (dual of [(2796201, 3), 8388562, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5⁴¹, large, F₅, 6) (dual of [large, large−41, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(5¹⁰⁰, 2796228, F₅, 3, 12) (dual of [(2796228, 3), 8388584, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁹, 27, F₅, 3, 6) (dual of [(27, 3), 72, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 9, 27)-net over F₅, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(5⁹¹, 2796201, F₅, 3, 12) (dual of [(2796201, 3), 8388512, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5⁹¹, large, F₅, 12) (dual of [large, large−91, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’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.