MinT - Information on Result #1538236

Information on Result #1538236

Linear OOA(4¹⁵⁶, 119671, F₄, 3, 23) (dual of [(119671, 3), 358857, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁵⁶, 119671, F₄, 2, 23) (dual of [(119671, 2), 239186, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁵⁶, 131082, F₄, 2, 23) (dual of [(131082, 2), 262008, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁵⁶, 262164, F₄, 23) (dual of [262164, 262008, 24]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(4¹⁵⁵, 262163, F₄, 23) (dual of [262163, 262008, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. linear OA(4¹⁵⁴, 262144, F₄, 23) (dual of [262144, 261990, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(4¹³⁶, 262144, F₄, 21) (dual of [262144, 262008, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(4¹, 19, F₄, 1) (dual of [19, 18, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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(4¹⁵⁶, 29917, F₄, 27, 23) (dual of [(29917, 27), 807603, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row