MinT - Information on Result #1455085

Information on Result #1455085

Linear OOA(16¹¹⁷, 108521, F₁₆, 2, 29) (dual of [(108521, 2), 216925, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16¹¹⁷, 108521, F₁₆, 29) (dual of [108521, 108404, 30]-code), using

discarding factors / shortening the dual code based on linear OA(16¹¹⁷, 131085, F₁₆, 29) (dual of [131085, 130968, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16¹¹⁶, 131084, F₁₆, 29) (dual of [131084, 130968, 30]-code), using
  - trace code [i] based on linear OA(256⁵⁸, 65542, F₂₅₆, 29) (dual of [65542, 65484, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,13]) [i] based on
      1. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      2. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 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(16¹¹⁷, 15502, F₁₆, 30, 29) (dual of [(15502, 30), 464943, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row