MinT - Information on Result #1196198

Information on Result #1196198

Digital (30, 42, 2614)-net over F₂₅, using net defined by OOA based on linear OOA(25⁴², 2614, F₂₅, 14, 12) (dual of [(2614, 14), 36554, 13]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁴², 7843, F₂₅, 2, 12) (dual of [(7843, 2), 15644, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁷, 27, F₂₅, 2, 6) (dual of [(27, 2), 47, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 27)-net over F₂₅, using
      - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
        Niederreiter sequence [i]
  2. linear OOA(25³⁵, 7816, F₂₅, 2, 12) (dual of [(7816, 2), 15597, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25³⁵, 15632, F₂₅, 12) (dual of [15632, 15597, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(9) [i] based on
        linear OA(25³⁴, 15625, F₂₅, 12) (dual of [15625, 15591, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(25²⁸, 15625, F₂₅, 10) (dual of [15625, 15597, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(25¹, 7, F₂₅, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.