MinT - Information on Result #1542811

Information on Result #1542811

Linear OOA(4²¹⁸, 118638, F₄, 3, 32) (dual of [(118638, 3), 355696, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²¹⁸, 118638, F₄, 2, 32) (dual of [(118638, 2), 237058, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²¹⁸, 131081, F₄, 2, 32) (dual of [(131081, 2), 261944, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²¹⁸, 262162, F₄, 32) (dual of [262162, 261944, 33]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²¹⁸, 262163, F₄, 32) (dual of [262163, 261945, 33]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(29) [i] based on
      1. linear OA(4²¹⁷, 262144, F₄, 33) (dual of [262144, 261927, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(4¹⁹⁹, 262144, F₄, 30) (dual of [262144, 261945, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [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(4²¹⁸, 19772, F₄, 39, 32) (dual of [(19772, 39), 770890, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row