MinT - Information on Result #1601607

Information on Result #1601607

Linear OOA(3⁶⁵, 265734, F₃, 4, 8) (dual of [(265734, 4), 1062871, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁶⁵, 265734, F₃, 2, 8) (dual of [(265734, 2), 531403, 9]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁶⁵, 531468, F₃, 8) (dual of [531468, 531403, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁶⁵, 531469, F₃, 8) (dual of [531469, 531404, 9]-code), using
  - constructionÂ X applied to C_e(7) âŠ‚ C_e(4) [i] based on
    1. linear OA(3⁶¹, 531441, F₃, 8) (dual of [531441, 531380, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. linear OA(3³⁷, 531441, F₃, 5) (dual of [531441, 531404, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(3⁴, 28, F₃, 2) (dual of [28, 24, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3⁶⁵, 265733, F₃, 5, 8) (dual of [(265733, 5), 1328600, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁶⁵, 265733, F₃, 12, 8) (dual of [(265733, 12), 3188731, 9]-NRT-code)	[i]		OOA Stacking with Additional Row