MinT - Information on Result #1021483

Information on Result #1021483

Linear OOA(5¹²⁹, 5592499, F₅, 3, 11) (dual of [(5592499, 3), 16777368, 12]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(5³, 31, F₅, 3, 2) (dual of [(31, 3), 90, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
    - Hamming code H(3,5) [i]
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]
linear OOA(5⁴⁰, 2796201, F₅, 3, 5) (dual of [(2796201, 3), 8388563, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5⁴⁰, 4194301, F₅, 3, 5) (dual of [(4194301, 3), 12582863, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(5⁴⁰, large, F₅, 5) (dual of [large, large−40, 6]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
linear OOA(5⁸¹, 2796201, F₅, 3, 11) (dual of [(2796201, 3), 8388522, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.