MinT - Information on Result #1188412

Information on Result #1188412

Digital (54, 63, 97671)-net over F₅, using net defined by OOA based on linear OOA(5⁶³, 97671, F₅, 10, 9) (dual of [(97671, 10), 976647, 10]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(5⁶³, 195343, F₅, 2, 9) (dual of [(195343, 2), 390623, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁶, 27, F₅, 2, 4) (dual of [(27, 2), 48, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 6, 27)-net over F₅, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(5⁵⁷, 195316, F₅, 2, 9) (dual of [(195316, 2), 390575, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(5⁵⁷, 390632, F₅, 9) (dual of [390632, 390575, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁵⁷, 390633, F₅, 9) (dual of [390633, 390576, 10]-code), using
        constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
        linear OA(5⁵⁷, 390625, F₅, 9) (dual of [390625, 390568, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(5⁴⁹, 390625, F₅, 8) (dual of [390625, 390576, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(5⁰, 8, F₅, 0) (dual of [8, 8, 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.