MinT - Information on Result #1021441

Information on Result #1021441

Linear OOA(5⁷⁷, 7289001, F₅, 3, 7) (dual of [(7289001, 3), 21866926, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(5¹, 1123200, F₅, 3, 1) (dual of [(1123200, 3), 3369599, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(5¹, 1123200, F₅, 3, 1) (dual of [(1123200, 3), 3369599, 2]-NRT-code) (see above)
linear OOA(5¹⁰, 1123200, F₅, 3, 2) (dual of [(1123200, 3), 3369590, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5¹⁰, 2441406, F₅, 3, 2) (dual of [(2441406, 3), 7324208, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(5¹⁰, 2441406, F₅, 2, 2) (dual of [(2441406, 2), 4882802, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(5¹⁰, 2441406, F₅, 2) (dual of [2441406, 2441396, 3]-code), using
      - Hamming code H(10,5) [i]
linear OOA(5¹⁴, 1123200, F₅, 3, 3) (dual of [(1123200, 3), 3369586, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹⁴, 1123200, F₅, 2, 3) (dual of [(1123200, 2), 2246386, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁴, 1123200, F₅, 3) (dual of [1123200, 1123186, 4]-code or 1123200-cap in PG(13,5)), using
    - product of two projective caps and an affine cap avoiding two hyperplanes [i] based on
      1. 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 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(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.