MinT - Information on Result #1195853

Information on Result #1195853

Linear OOA(25²⁶, 4882949, F₂₅, 6, 5) (dual of [(4882949, 6), 29297668, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(25²⁶, 4882950, F₂₅, 2, 5) (dual of [(4882950, 2), 9765874, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(25⁰, s, F₂₅, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
3. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
4. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
5. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
6. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
7. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
8. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
9. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
10. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
11. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
12. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
13. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
14. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
15. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
16. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
17. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
18. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
19. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
20. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
21. linear OOA(25¹, 195318, F₂₅, 2, 1) (dual of [(195318, 2), 390635, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(25¹, s, F₂₅, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
22. linear OOA(25¹, 195318, F₂₅, 2, 1) (dual of [(195318, 2), 390635, 2]-NRT-code) (see above)
23. linear OOA(25¹, 195318, F₂₅, 2, 1) (dual of [(195318, 2), 390635, 2]-NRT-code) (see above)
24. linear OOA(25⁵, 195318, F₂₅, 2, 2) (dual of [(195318, 2), 390631, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(25⁵, 406901, F₂₅, 2, 2) (dual of [(406901, 2), 813797, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(25⁵, 406901, F₂₅, 2) (dual of [406901, 406896, 3]-code), using
      - Hamming code H(5,25) [i]
25. linear OOA(25¹⁸, 195318, F₂₅, 2, 5) (dual of [(195318, 2), 390618, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(25¹⁸, 390636, F₂₅, 5) (dual of [390636, 390618, 6]-code), using
    - constructionÂ X4 applied to C([0,2]) âŠ‚ C([0,1]) [i] based on
      1. linear OA(25¹⁷, 390626, F₂₅, 5) (dual of [390626, 390609, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      2. linear OA(25⁹, 390626, F₂₅, 3) (dual of [390626, 390617, 4]-code or 390626-cap in PG(8,25)), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,1], and minimum distance dÂ â‰¥ |{−1,0,1}|+1Â =Â 4 (BCH-bound) [i]
      3. linear OA(25⁹, 10, F₂₅, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
        dual of repetition code with length 10 [i]
      4. linear OA(25¹, 10, F₂₅, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, 25, F₂₅, 1) (dual of [25, 24, 2]-code), using
        Reedâ€“Solomon code RS(24,25) [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (21, 26, 4882949)-net over F₂₅	[i]		Net Defined by OOA