MinT - Information on Result #1545947

Information on Result #1545947

Linear OOA(4²⁵¹, 115733, F₄, 3, 37) (dual of [(115733, 3), 346948, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁵¹, 115733, F₄, 2, 37) (dual of [(115733, 2), 231215, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁵¹, 131089, F₄, 2, 37) (dual of [(131089, 2), 261927, 38]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4²⁴⁹, 131088, F₄, 2, 37) (dual of [(131088, 2), 261927, 38]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁴⁹, 262176, F₄, 37) (dual of [262176, 261927, 38]-code), using
    - constructionÂ X applied to C_e(36) âŠ‚ C_e(32) [i] based on
      1. linear OA(4²⁴⁴, 262144, F₄, 37) (dual of [262144, 261900, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
      2. 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]
      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(4²⁵¹, 19288, F₄, 39, 37) (dual of [(19288, 39), 751981, 38]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row