MinT - Information on Result #1188318

Information on Result #1188318

Digital (34, 42, 3913)-net over F₅, using net defined by OOA based on linear OOA(5⁴², 3913, F₅, 10, 8) (dual of [(3913, 10), 39088, 9]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(5⁴², 7827, F₅, 2, 8) (dual of [(7827, 2), 15612, 9]-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(5³⁷, 7815, F₅, 2, 8) (dual of [(7815, 2), 15593, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(5³⁷, 15630, F₅, 8) (dual of [15630, 15593, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(5³⁷, 15631, F₅, 8) (dual of [15631, 15594, 9]-code), using
        constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        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(5³¹, 15625, F₅, 7) (dual of [15625, 15594, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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.