MinT - Information on Result #1651498

Information on Result #1651498

Linear OOA(3²³⁸, 155406, F₃, 5, 29) (dual of [(155406, 5), 776792, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁸, 155406, F₃, 3, 29) (dual of [(155406, 3), 465980, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁸, 177162, F₃, 3, 29) (dual of [(177162, 3), 531248, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3²³⁵, 177161, F₃, 3, 29) (dual of [(177161, 3), 531248, 30]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²³⁵, 531483, F₃, 29) (dual of [531483, 531248, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(24) [i] based on
      1. linear OA(3²²⁹, 531441, F₃, 29) (dual of [531441, 531212, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁹³, 531441, F₃, 25) (dual of [531441, 531248, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(3²³⁸, 51801, F₃, 35, 29) (dual of [(51801, 35), 1812797, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row