MinT - Information on Result #1012955

Information on Result #1012955

Linear OOA(5⁷², 5592774, F₅, 3, 7) (dual of [(5592774, 3), 16778250, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁵, 3050326, F₅, 3, 3) (dual of [(3050326, 3), 9150963, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹⁵, 3050326, F₅, 2, 3) (dual of [(3050326, 2), 6100637, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁵, 3050326, F₅, 3) (dual of [3050326, 3050311, 4]-code or 3050326-cap in PG(14,5)), using
    - product of projective cap with cap in AG(6,Â 5) [i] based on linear OA(5⁹, 4700, F₅, 3) (dual of [4700, 4691, 4]-code or 4700-cap in PG(8,5)), using
      - caps completed using a computer search [i]
linear OOA(5⁵⁷, 2796387, F₅, 3, 7) (dual of [(2796387, 3), 8389104, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁶, 186, F₅, 3, 3) (dual of [(186, 3), 552, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5⁶, 186, F₅, 2, 3) (dual of [(186, 2), 366, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁶, 186, F₅, 3) (dual of [186, 180, 4]-code or 186-cap in PG(5,5)), using
        caps completed using a computer search [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.

Other Results with Identical Parameters

None.

Depending Results

None.