MinT - Information on Result #1453316

Information on Result #1453316

Linear OOA(16⁵¹, 97313, F₁₆, 2, 13) (dual of [(97313, 2), 194575, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁵¹, 97313, F₁₆, 13) (dual of [97313, 97262, 14]-code), using

discarding factors / shortening the dual code based on linear OA(16⁵¹, 131077, F₁₆, 13) (dual of [131077, 131026, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁵⁰, 131076, F₁₆, 13) (dual of [131076, 131026, 14]-code), using
  - trace code [i] based on linear OA(256²⁵, 65538, F₂₅₆, 13) (dual of [65538, 65513, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(256²⁵, 65536, F₂₅₆, 13) (dual of [65536, 65511, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(256²³, 65536, F₂₅₆, 12) (dual of [65536, 65513, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(16⁵¹, 32437, F₁₆, 14, 13) (dual of [(32437, 14), 454067, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row