MinT - Information on Result #1364770

Information on Result #1364770

Linear OOA(4⁸⁴, 524301, F₄, 2, 11) (dual of [(524301, 2), 1048518, 12]-NRT-code), using OOA 2-folding based on linear OA(4⁸⁴, 1048602, F₄, 11) (dual of [1048602, 1048518, 12]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(4⁸², 1048599, F₄, 11) (dual of [1048599, 1048517, 12]-code), using
  - constructionÂ X4 applied to C([0,5]) âŠ‚ C([0,4]) [i] based on
    1. linear OA(4⁸¹, 1048577, F₄, 11) (dual of [1048577, 1048496, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
    2. linear OA(4⁶¹, 1048577, F₄, 9) (dual of [1048577, 1048516, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    3. linear OA(4²¹, 22, F₄, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
      - dual of repetition code with length 22 [i]
    4. linear OA(4¹, 22, F₄, 1) (dual of [22, 21, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(4⁸², 1048600, F₄, 9) (dual of [1048600, 1048518, 10]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4⁸²Â > V_b^sâˆ’1(kâˆ’1)Â = 237856 232576 187549 974856 024211 765017 061338 727546 [i]
3. linear OA(4¹, 2, F₄, 1) (dual of [2, 1, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)

Mode: 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(4⁸⁴, 524301, F₄, 3, 11) (dual of [(524301, 3), 1572819, 12]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (73, 84, 524301)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound