MinT - Information on Result #1538748

Information on Result #1538748

Linear OOA(4¹⁶⁴, 127579, F₄, 3, 24) (dual of [(127579, 3), 382573, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁶⁴, 127579, F₄, 2, 24) (dual of [(127579, 2), 254994, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁶⁴, 131081, F₄, 2, 24) (dual of [(131081, 2), 261998, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁶⁴, 262162, F₄, 24) (dual of [262162, 261998, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁴, 262163, F₄, 24) (dual of [262163, 261999, 25]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(4¹⁶³, 262144, F₄, 25) (dual of [262144, 261981, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(4¹⁴⁵, 262144, F₄, 22) (dual of [262144, 261999, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(4¹⁶⁴, 31894, F₄, 27, 24) (dual of [(31894, 27), 860974, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row