MinT - Information on Result #1188778

Information on Result #1188778

Digital (57, 70, 2618)-net over F₅, using net defined by OOA based on linear OOA(5⁷⁰, 2618, F₅, 15, 13) (dual of [(2618, 15), 39200, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(5⁷⁰, 5237, F₅, 3, 13) (dual of [(5237, 3), 15641, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁹, 27, F₅, 3, 6) (dual of [(27, 3), 72, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 9, 27)-net over F₅, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(5⁶¹, 5210, F₅, 3, 13) (dual of [(5210, 3), 15569, 14]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5⁶¹, 15630, F₅, 13) (dual of [15630, 15569, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁶¹, 15631, F₅, 13) (dual of [15631, 15570, 14]-code), using
        constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(5⁶¹, 15625, F₅, 13) (dual of [15625, 15564, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(5⁵⁵, 15625, F₅, 12) (dual of [15625, 15570, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.