MinT - Information on Result #899521

Information on Result #899521

Linear OOA(25⁴⁵, 7843, F₂₅, 2, 13) (dual of [(7843, 2), 15641, 14]-NRT-code), using (u,Â u+v)-construction based on

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]
linear OOA(25³⁸, 7816, F₂₅, 2, 13) (dual of [(7816, 2), 15594, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25³⁸, 15632, F₂₅, 13) (dual of [15632, 15594, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(25³⁸, 15633, F₂₅, 13) (dual of [15633, 15595, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,5]) [i] based on
      1. linear OA(25³⁷, 15626, F₂₅, 13) (dual of [15626, 15589, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626Â | 25⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      2. linear OA(25³¹, 15626, F₂₅, 11) (dual of [15626, 15595, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626Â | 25⁶âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      3. 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, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25⁴⁵, 2614, F₂₅, 14, 13) (dual of [(2614, 14), 36551, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row