MinT - Information on Result #1646387

Information on Result #1646387

Linear OOA(3¹⁷⁷, 20101, F₃, 5, 26) (dual of [(20101, 5), 100328, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁷, 20101, F₃, 2, 26) (dual of [(20101, 2), 40025, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁷, 29542, F₃, 2, 26) (dual of [(29542, 2), 58907, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁷⁷, 59084, F₃, 26) (dual of [59084, 58907, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁷⁷, 59085, F₃, 26) (dual of [59085, 58908, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
      1. linear OA(3¹⁷¹, 59049, F₃, 26) (dual of [59049, 58878, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(3⁶, 36, F₃, 3) (dual of [36, 30, 4]-code or 36-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(3¹⁷⁷, 6700, F₃, 35, 26) (dual of [(6700, 35), 234323, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row