MinT - Information on Result #1364772

Information on Result #1364772

Linear OOA(4⁹², 2097166, F₄, 2, 11) (dual of [(2097166, 2), 4194240, 12]-NRT-code), using OOA 2-folding based on linear OA(4⁹², 4194332, F₄, 11) (dual of [4194332, 4194240, 12]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(4⁹⁰, 4194329, F₄, 11) (dual of [4194329, 4194239, 12]-code), using
  - constructionÂ X4 applied to C([0,5]) âŠ‚ C([0,4]) [i] based on
    1. linear OA(4⁸⁹, 4194305, F₄, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
    2. linear OA(4⁶⁷, 4194305, F₄, 9) (dual of [4194305, 4194238, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    3. linear OA(4²³, 24, F₄, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
      - dual of repetition code with length 24 [i]
    4. linear OA(4¹, 24, F₄, 1) (dual of [24, 23, 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(4⁹⁰, 4194330, F₄, 9) (dual of [4194330, 4194240, 10]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4⁹⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 15586 436580 914441 471956 621644 321929 588584 783055 727931 [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(4⁹², 2097166, F₄, 3, 11) (dual of [(2097166, 3), 6291406, 12]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (81, 92, 2097166)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound