MinT - Information on Result #1324108

Information on Result #1324108

Linear OA(4²¹⁹, 1048656, F₄, 27) (dual of [1048656, 1048437, 28]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4²¹⁶, 1048652, F₄, 27) (dual of [1048652, 1048436, 28]-code), using
- constructionÂ X applied to C([0,13]) âŠ‚ C([0,9]) [i] based on
  1. linear OA(4²⁰¹, 1048577, F₄, 27) (dual of [1048577, 1048376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
  2. linear OA(4¹⁴¹, 1048577, F₄, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
  3. linear OA(4¹⁵, 75, F₄, 7) (dual of [75, 60, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁵, 85, F₄, 7) (dual of [85, 70, 8]-code), using
      - a code from Grasslâ€™s database [i]
linear OA(4²¹⁶, 1048653, F₄, 24) (dual of [1048653, 1048437, 25]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²¹⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 10 857123 643294 049768 057150 883313 310727 122807 343457 659303 482536 811682 533672 526978 818693 571590 009140 873205 445290 759226 509693 288296 [i]
linear OA(4², 3, F₄, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²¹⁹, 524328, F₄, 2, 27) (dual of [(524328, 2), 1048437, 28]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4²¹⁹, 349552, F₄, 3, 27) (dual of [(349552, 3), 1048437, 28]-NRT-code)	[i]		OOA Folding