MinT - Information on Result #1543257

Information on Result #1543257

Linear OOA(4²²³, 109332, F₄, 3, 33) (dual of [(109332, 3), 327773, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²²³, 109332, F₄, 2, 33) (dual of [(109332, 2), 218441, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²²³, 131088, F₄, 2, 33) (dual of [(131088, 2), 261953, 34]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²²², 131088, F₄, 2, 33) (dual of [(131088, 2), 261954, 34]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²²², 262176, F₄, 33) (dual of [262176, 261954, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(28) [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(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(4⁵, 32, F₄, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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(4²²³, 18221, F₄, 39, 33) (dual of [(18221, 39), 710396, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row