MinT - Information on Result #1299978

Information on Result #1299978

Linear OA(4⁹³, 16422, F₄, 16) (dual of [16422, 16329, 17]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4⁹², 16420, F₄, 16) (dual of [16420, 16328, 17]-code), using
- constructionÂ X applied to C([0,8]) âŠ‚ C([0,5]) [i] based on
  1. linear OA(4⁸⁵, 16385, F₄, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 4¹⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  2. linear OA(4⁵⁷, 16385, F₄, 11) (dual of [16385, 16328, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 4¹⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
  3. linear OA(4⁷, 35, F₄, 4) (dual of [35, 28, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁷, 43, F₄, 4) (dual of [43, 36, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]
linear OA(4⁹², 16421, F₄, 15) (dual of [16421, 16329, 16]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4⁹²Â > V_b^sâˆ’1(kâˆ’1)Â = 5 652354 159452 762794 943295 205529 835421 377288 577081 100392 [i]
linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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(4⁹³, 16422, F₄, 2, 16) (dual of [(16422, 2), 32751, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4⁹³, 16422, F₄, 3, 16) (dual of [(16422, 3), 49173, 17]-NRT-code)	[i]
3	Digital (77, 93, 16422)-net over F₄	[i]
4	Linear OOA(4⁹³, 8211, F₄, 2, 16) (dual of [(8211, 2), 16329, 17]-NRT-code)	[i]	OOA Folding