MinT - Information on Result #1453770

Information on Result #1453770

Linear OOA(16⁷⁵, 83420, F₁₆, 2, 19) (dual of [(83420, 2), 166765, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁷⁵, 83420, F₁₆, 19) (dual of [83420, 83345, 20]-code), using

discarding factors / shortening the dual code based on linear OA(16⁷⁵, 131077, F₁₆, 19) (dual of [131077, 131002, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁷⁴, 131076, F₁₆, 19) (dual of [131076, 131002, 20]-code), using
  - trace code [i] based on linear OA(256³⁷, 65538, F₂₅₆, 19) (dual of [65538, 65501, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
      1. linear OA(256³⁷, 65536, F₂₅₆, 19) (dual of [65536, 65499, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(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(16⁷⁵, 16683, F₁₆, 22, 19) (dual of [(16683, 22), 366951, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row