MinT - Information on Result #1603875

Information on Result #1603875

Linear OOA(3¹²⁷, 246789, F₃, 4, 15) (dual of [(246789, 4), 987029, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²⁷, 246789, F₃, 2, 15) (dual of [(246789, 2), 493451, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²⁷, 265741, F₃, 2, 15) (dual of [(265741, 2), 531355, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²⁷, 531482, F₃, 15) (dual of [531482, 531355, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁷, 531483, F₃, 15) (dual of [531483, 531356, 16]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
      1. linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(3⁸⁵, 531441, F₃, 11) (dual of [531441, 531356, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3¹²⁷, 123394, F₃, 20, 15) (dual of [(123394, 20), 2467753, 16]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row