MinT - Information on Result #2495632

Information on Result #2495632

Linear OOA(4¹³¹, 131084, F₄, 2, 19) (dual of [(131084, 2), 262037, 20]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹²⁹, 131083, F₄, 2, 19) (dual of [(131083, 2), 262037, 20]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹²⁹, 262166, F₄, 19) (dual of [262166, 262037, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹²⁸, 262165, F₄, 19) (dual of [262165, 262037, 20]-code), using
  - constructionÂ X4 applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(4¹²⁷, 262145, F₄, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    2. linear OA(4¹⁰⁹, 262145, F₄, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    3. linear OA(4¹⁹, 20, F₄, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
      - dual of repetition code with length 20 [i]
    4. linear OA(4¹, 20, F₄, 1) (dual of [20, 19, 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]

Mode: Constructive and 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(4¹³¹, 131084, F₄, 3, 19) (dual of [(131084, 3), 393121, 20]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (112, 131, 131084)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound