MinT - Information on Result #1188390

Information on Result #1188390

Digital (39, 48, 3913)-net over F₅, using net defined by OOA based on linear OOA(5⁴⁸, 3913, F₅, 10, 9) (dual of [(3913, 10), 39082, 10]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(5⁴⁸, 7827, F₅, 2, 9) (dual of [(7827, 2), 15606, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁵, 12, F₅, 2, 4) (dual of [(12, 2), 19, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 5, 12)-net over F₅, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(5⁴³, 7815, F₅, 2, 9) (dual of [(7815, 2), 15587, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(5⁴³, 15630, F₅, 9) (dual of [15630, 15587, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁴³, 15631, F₅, 9) (dual of [15631, 15588, 10]-code), using
        constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
        linear OA(5⁴³, 15625, F₅, 9) (dual of [15625, 15582, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(5³⁷, 15625, F₅, 8) (dual of [15625, 15588, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(5⁰, 6, F₅, 0) (dual of [6, 6, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.