MinT - Information on Result #1529597

Information on Result #1529597

Linear OOA(3²¹⁵, 5714, F₃, 3, 37) (dual of [(5714, 3), 16927, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²¹⁵, 5714, F₃, 37) (dual of [5714, 5499, 38]-code), using

discarding factors / shortening the dual code based on linear OA(3²¹⁵, 6631, F₃, 37) (dual of [6631, 6416, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²¹⁴, 6630, F₃, 37) (dual of [6630, 6416, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(27) [i] based on
    1. linear OA(3¹⁹³, 6561, F₃, 37) (dual of [6561, 6368, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    2. linear OA(3¹⁴⁵, 6561, F₃, 28) (dual of [6561, 6416, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(3²¹, 69, F₃, 8) (dual of [69, 48, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(3²¹, 80, F₃, 8) (dual of [80, 59, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(3²¹⁵, 2857, F₃, 5, 37) (dual of [(2857, 5), 14070, 38]-NRT-code)	[i]		OOA Folding