MinT - Information on Result #1527764

Information on Result #1527764

Linear OOA(3¹⁹⁶, 25624, F₃, 3, 28) (dual of [(25624, 3), 76676, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁶, 25624, F₃, 2, 28) (dual of [(25624, 2), 51052, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹⁶, 29552, F₃, 2, 28) (dual of [(29552, 2), 58908, 29]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁹², 29550, F₃, 2, 28) (dual of [(29550, 2), 58908, 29]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁹², 59100, F₃, 28) (dual of [59100, 58908, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [i] based on
      1. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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(3¹¹, 51, F₃, 5) (dual of [51, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3¹⁹⁶, 12812, F₃, 5, 28) (dual of [(12812, 5), 63864, 29]-NRT-code)	[i]		OOA Folding