MinT - Information on Result #899810

Information on Result #899810

Linear OOA(25⁸³, 195341, F₂₅, 2, 19) (dual of [(195341, 2), 390599, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁰, 27, F₂₅, 2, 9) (dual of [(27, 2), 44, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 10, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]
linear OOA(25⁷³, 195314, F₂₅, 2, 19) (dual of [(195314, 2), 390555, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷³, 390628, F₂₅, 19) (dual of [390628, 390555, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷³, 390629, F₂₅, 19) (dual of [390629, 390556, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
      1. linear OA(25⁷³, 390625, F₂₅, 19) (dual of [390625, 390552, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(25⁶⁹, 390625, F₂₅, 18) (dual of [390625, 390556, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.