MinT - Information on Result #1301569

Information on Result #1301569

Linear OA(5⁹⁰, 15668, F₅, 17) (dual of [15668, 15578, 18]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁸⁸, 15664, F₅, 17) (dual of [15664, 15576, 18]-code), using
- constructionÂ X applied to C_e(16) âŠ‚ C_e(10) [i] based on
  1. linear OA(5⁷⁹, 15625, F₅, 17) (dual of [15625, 15546, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  2. linear OA(5⁴⁹, 15625, F₅, 11) (dual of [15625, 15576, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(5⁹, 39, F₅, 5) (dual of [39, 30, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁹, 44, F₅, 5) (dual of [44, 35, 6]-code), using
      - codes constructed by inverting constructionÂ Y₁ [i]
linear OA(5⁸⁸, 15666, F₅, 16) (dual of [15666, 15578, 17]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁸⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 684775 809621 949114 753214 447816 544653 717646 047568 928814 544965 [i]
linear OA(5⁰, 2, F₅, 0) (dual of [2, 2, 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(5⁹⁰, 15668, F₅, 2, 17) (dual of [(15668, 2), 31246, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(5⁹⁰, 15668, F₅, 3, 17) (dual of [(15668, 3), 46914, 18]-NRT-code)	[i]
3	Digital (73, 90, 15668)-net over F₅	[i]
4	Linear OOA(5⁹⁰, 7834, F₅, 2, 17) (dual of [(7834, 2), 15578, 18]-NRT-code)	[i]	OOA Folding