MinT - Information on Result #1453968

Information on Result #1453968

Linear OOA(16⁸³, 83138, F₁₆, 2, 21) (dual of [(83138, 2), 166193, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16⁸³, 83138, F₁₆, 21) (dual of [83138, 83055, 22]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸³, 131077, F₁₆, 21) (dual of [131077, 130994, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁸², 131076, F₁₆, 21) (dual of [131076, 130994, 22]-code), using
  - trace code [i] based on linear OA(256⁴¹, 65538, F₂₅₆, 21) (dual of [65538, 65497, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
      1. linear OA(256⁴¹, 65536, F₂₅₆, 21) (dual of [65536, 65495, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. 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]
      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(16⁸³, 16627, F₁₆, 22, 21) (dual of [(16627, 22), 365711, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row