MinT - Information on Result #1301678

Information on Result #1301678

Linear OA(5¹⁰³, 390665, F₅, 15) (dual of [390665, 390562, 16]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹⁰², 390663, F₅, 15) (dual of [390663, 390561, 16]-code), using
- constructionÂ X applied to C([0,7]) âŠ‚ C([0,5]) [i] based on
  1. linear OA(5⁹⁷, 390626, F₅, 15) (dual of [390626, 390529, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 5¹⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
  2. linear OA(5⁶⁵, 390626, F₅, 11) (dual of [390626, 390561, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 5¹⁶âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
  3. linear OA(5⁵, 37, F₅, 3) (dual of [37, 32, 4]-code or 37-cap in PG(4,5)), using
    - discarding factors / shortening the dual code based on linear OA(5⁵, 42, F₅, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
      - large caps in PG(4,Â b) [i]
linear OA(5¹⁰², 390664, F₅, 14) (dual of [390664, 390562, 15]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹⁰²Â > V_b^sâˆ’1(kâˆ’1)Â = 53191 975752 600882 847800 129453 853790 460514 506906 867017 436994 682898 561325 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 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(5¹⁰³, 390665, F₅, 2, 15) (dual of [(390665, 2), 781227, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(5¹⁰³, 390665, F₅, 3, 15) (dual of [(390665, 3), 1171892, 16]-NRT-code)	[i]
3	Digital (88, 103, 390665)-net over F₅	[i]