MinT - Information on Result #896314

Information on Result #896314

Linear OOA(7⁴⁸, 58840, F₇, 2, 9) (dual of [(58840, 2), 117632, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁵, 13, F₇, 2, 4) (dual of [(13, 2), 21, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 5, 13)-net over F₇, using
  - 8 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁴³, 58827, F₇, 2, 9) (dual of [(58827, 2), 117611, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(7⁴³, 117654, F₇, 9) (dual of [117654, 117611, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁴³, 117655, F₇, 9) (dual of [117655, 117612, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(7⁴³, 117649, F₇, 9) (dual of [117649, 117606, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 7⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(7³⁷, 117649, F₇, 8) (dual of [117649, 117612, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 7⁶âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(7⁰, 6, F₇, 0) (dual of [6, 6, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁴⁸, 29419, F₇, 10, 9) (dual of [(29419, 10), 294142, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row