MinT - Information on Result #1651890

Information on Result #1651890

Linear OOA(3²⁴², 427874, F₃, 5, 27) (dual of [(427874, 5), 2139128, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴², 427874, F₃, 3, 27) (dual of [(427874, 3), 1283380, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴², 531456, F₃, 3, 27) (dual of [(531456, 3), 1594126, 28]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁴¹, 531456, F₃, 3, 27) (dual of [(531456, 3), 1594127, 28]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²⁴¹, 1594368, F₃, 27) (dual of [1594368, 1594127, 28]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(22) [i] based on
      1. linear OA(3²³⁵, 1594323, F₃, 28) (dual of [1594323, 1594088, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(3¹⁹⁶, 1594323, F₃, 23) (dual of [1594323, 1594127, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3²⁴², 142624, F₃, 35, 27) (dual of [(142624, 35), 4991598, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row