MinT - Information on Result #1606173

Information on Result #1606173

Linear OOA(3¹⁶⁷, 24317, F₃, 4, 24) (dual of [(24317, 4), 97101, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁷, 24317, F₃, 2, 24) (dual of [(24317, 2), 48467, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁷, 29542, F₃, 2, 24) (dual of [(29542, 2), 58917, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁷, 59084, F₃, 24) (dual of [59084, 58917, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁷, 59085, F₃, 24) (dual of [59085, 58918, 25]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(19) [i] based on
      1. linear OA(3¹⁶¹, 59049, F₃, 25) (dual of [59049, 58888, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(3¹³¹, 59049, F₃, 20) (dual of [59049, 58918, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(3¹⁶⁷, 8105, F₃, 28, 24) (dual of [(8105, 28), 226773, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row