MinT - Information on Result #1603824

Information on Result #1603824

Linear OOA(3¹²⁶, 586725, F₃, 4, 14) (dual of [(586725, 4), 2346774, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²⁶, 586725, F₃, 2, 14) (dual of [(586725, 2), 1173324, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²⁶, 797185, F₃, 2, 14) (dual of [(797185, 2), 1594244, 15]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹²⁴, 797184, F₃, 2, 14) (dual of [(797184, 2), 1594244, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹²⁴, 1594368, F₃, 14) (dual of [1594368, 1594244, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(9) [i] based on
      1. linear OA(3¹¹⁸, 1594323, F₃, 14) (dual of [1594323, 1594205, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(3⁷⁹, 1594323, F₃, 10) (dual of [1594323, 1594244, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3⁶, 45, F₃, 3) (dual of [45, 39, 4]-code or 45-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(3¹²⁶, 293362, F₃, 20, 14) (dual of [(293362, 20), 5867114, 15]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row