MinT - Information on Result #1453918

Information on Result #1453918

Linear OOA(16⁸¹, 113148, F₁₆, 2, 20) (dual of [(113148, 2), 226215, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁸¹, 113148, F₁₆, 20) (dual of [113148, 113067, 21]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸¹, 131083, F₁₆, 20) (dual of [131083, 131002, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁸⁰, 131082, F₁₆, 20) (dual of [131082, 131002, 21]-code), using
  - trace code [i] based on linear OA(256⁴⁰, 65541, F₂₅₆, 20) (dual of [65541, 65501, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(17) [i] based on
      1. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(256³⁵, 65536, F₂₅₆, 18) (dual of [65536, 65501, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(16⁸¹, 22629, F₁₆, 22, 20) (dual of [(22629, 22), 497757, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row