MinT - Information on Result #1454927

Information on Result #1454927

Linear OOA(16¹¹³, 108175, F₁₆, 2, 28) (dual of [(108175, 2), 216237, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16¹¹³, 108175, F₁₆, 28) (dual of [108175, 108062, 29]-code), using

discarding factors / shortening the dual code based on linear OA(16¹¹³, 131083, F₁₆, 28) (dual of [131083, 130970, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16¹¹², 131082, F₁₆, 28) (dual of [131082, 130970, 29]-code), using
  - trace code [i] based on linear OA(256⁵⁶, 65541, F₂₅₆, 28) (dual of [65541, 65485, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(25) [i] based on
      1. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(256⁵¹, 65536, F₂₅₆, 26) (dual of [65536, 65485, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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(16¹¹³, 15453, F₁₆, 30, 28) (dual of [(15453, 30), 463477, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row