MinT - Information on Result #1537516

Information on Result #1537516

Linear OOA(4¹⁴⁴, 131089, F₄, 3, 21) (dual of [(131089, 3), 393123, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁴⁴, 131089, F₄, 2, 21) (dual of [(131089, 2), 262034, 22]-NRT-code), using

4¹ times duplication [i] based on linear OOA(4¹⁴³, 131089, F₄, 2, 21) (dual of [(131089, 2), 262035, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁴¹, 131088, F₄, 2, 21) (dual of [(131088, 2), 262035, 22]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁴¹, 262176, F₄, 21) (dual of [262176, 262035, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(16) [i] based on
      1. 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]
      2. linear OA(4¹⁰⁹, 262144, F₄, 17) (dual of [262144, 262035, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(4¹⁴⁴, 32772, F₄, 27, 21) (dual of [(32772, 27), 884700, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row