MinT - Information on Result #1012962

Information on Result #1012962

Linear OOA(5⁷⁸, 8388602, F₅, 3, 7) (dual of [(8388602, 3), 25165728, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁶, large, F₅, 3, 3), using
- appending kth column [i] based on linear OOA(5¹⁶, large, F₅, 2, 3), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁶, large, F₅, 3) (dual of [large, large−16, 4]-code), using
    - product of projective cap with 5²-ovoid cap in AG(3,Â 5) [i] based on linear OA(5¹³, 438101, F₅, 3) (dual of [438101, 438088, 4]-code or 438101-cap in PG(12,5)), using
      - product of projective cap with cap in AG(6,Â 5) [i] based on linear OA(5⁷, 675, F₅, 3) (dual of [675, 668, 4]-code or 675-cap in PG(6,5)), using
        product of two caps with tangent hyperplane [i]
linear OOA(5⁶², 4194301, F₅, 3, 7) (dual of [(4194301, 3), 12582841, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(5⁶², 8388602, F₅, 2, 7) (dual of [(8388602, 2), 16777142, 8]-NRT-code), using
  - trace code [i] based on linear OOA(25³¹, 4194301, F₂₅, 2, 7) (dual of [(4194301, 2), 8388571, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25³¹, 8388602, F₂₅, 7) (dual of [8388602, 8388571, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(25³¹, large, F₂₅, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [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.