MinT - Information on Result #1454500

Information on Result #1454500

Linear OOA(16¹⁰¹, 108049, F₁₆, 2, 25) (dual of [(108049, 2), 215997, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16¹⁰¹, 108049, F₁₆, 25) (dual of [108049, 107948, 26]-code), using

discarding factors / shortening the dual code based on linear OA(16¹⁰¹, 131085, F₁₆, 25) (dual of [131085, 130984, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16¹⁰⁰, 131084, F₁₆, 25) (dual of [131084, 130984, 26]-code), using
  - trace code [i] based on linear OA(256⁵⁰, 65542, F₂₅₆, 25) (dual of [65542, 65492, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,11]) [i] based on
      1. linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (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(16¹⁰¹, 18008, F₁₆, 26, 25) (dual of [(18008, 26), 468107, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row