MinT - Information on Result #1540100

Information on Result #1540100

Linear OOA(4¹⁸⁴, 120170, F₄, 3, 27) (dual of [(120170, 3), 360326, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁸⁴, 120170, F₄, 2, 27) (dual of [(120170, 2), 240156, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸⁴, 131083, F₄, 2, 27) (dual of [(131083, 2), 261982, 28]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁸², 131082, F₄, 2, 27) (dual of [(131082, 2), 261982, 28]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁸², 262164, F₄, 27) (dual of [262164, 261982, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(4¹⁸¹, 262145, F₄, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(4¹⁶³, 262145, F₄, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      3. linear OA(4¹, 19, F₄, 1) (dual of [19, 18, 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: 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(4¹⁸⁴, 24033, F₄, 33, 27) (dual of [(24033, 33), 792905, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row