MinT - Information on Result #1195844

Information on Result #1195844

Digital (15, 20, 195964)-net over F₂₅, using net defined by OOA based on linear OOA(25²⁰, 195964, F₂₅, 6, 5) (dual of [(195964, 6), 1175764, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(25²⁰, 195965, F₂₅, 2, 5) (dual of [(195965, 2), 391910, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25³, 651, F₂₅, 2, 2) (dual of [(651, 2), 1299, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(25³, 651, F₂₅, 2) (dual of [651, 648, 3]-code), using
      - Hamming code H(3,25) [i]
  2. linear OOA(25¹⁷, 195314, F₂₅, 2, 5) (dual of [(195314, 2), 390611, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25¹⁷, 390628, F₂₅, 5) (dual of [390628, 390611, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(25¹⁷, 390629, F₂₅, 5) (dual of [390629, 390612, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(25¹⁷, 390625, F₂₅, 5) (dual of [390625, 390608, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(25¹³, 390625, F₂₅, 4) (dual of [390625, 390612, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(25⁰, 4, F₂₅, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 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.