MinT - Information on Result #896092

Information on Result #896092

Linear OOA(5⁴⁹, 7842, F₅, 2, 9) (dual of [(7842, 2), 15635, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5⁶, 27, F₅, 2, 4) (dual of [(27, 2), 48, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 6, 27)-net over F₅, using
  - linear code embedding found in a computer search [i]
linear OOA(5⁴³, 7815, F₅, 2, 9) (dual of [(7815, 2), 15587, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5⁴³, 15630, F₅, 9) (dual of [15630, 15587, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁴³, 15631, F₅, 9) (dual of [15631, 15588, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(5⁴³, 15625, F₅, 9) (dual of [15625, 15582, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(5³⁷, 15625, F₅, 8) (dual of [15625, 15588, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(5⁰, 6, F₅, 0) (dual of [6, 6, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5⁴⁹, 3920, F₅, 10, 9) (dual of [(3920, 10), 39151, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row