MinT - Information on Result #1607665

Information on Result #1607665

Linear OOA(3¹⁸⁸, 175305, F₃, 4, 23) (dual of [(175305, 4), 701032, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁸, 175305, F₃, 3, 23) (dual of [(175305, 3), 525727, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁸, 177161, F₃, 3, 23) (dual of [(177161, 3), 531295, 24]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁸⁷, 177161, F₃, 3, 23) (dual of [(177161, 3), 531296, 24]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁸⁷, 531483, F₃, 23) (dual of [531483, 531296, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
      1. linear OA(3¹⁸¹, 531441, F₃, 23) (dual of [531441, 531260, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(3¹⁴⁵, 531441, F₃, 19) (dual of [531441, 531296, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(3⁶, 42, F₃, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3¹⁸⁸, 58434, F₃, 28, 23) (dual of [(58434, 28), 1635964, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row