MinT - Information on Result #1650382

Information on Result #1650382

Linear OOA(3²²⁶, 9382, F₃, 5, 37) (dual of [(9382, 5), 46684, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁶, 9382, F₃, 2, 37) (dual of [(9382, 2), 18538, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁶, 9859, F₃, 2, 37) (dual of [(9859, 2), 19492, 38]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²²⁵, 9859, F₃, 2, 37) (dual of [(9859, 2), 19493, 38]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²²⁵, 19718, F₃, 37) (dual of [19718, 19493, 38]-code), using
    - constructionÂ X applied to C_e(36) âŠ‚ C_e(31) [i] based on
      1. linear OA(3²¹⁷, 19683, F₃, 37) (dual of [19683, 19466, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
      2. linear OA(3¹⁹⁰, 19683, F₃, 32) (dual of [19683, 19493, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
      3. linear OA(3⁸, 35, F₃, 4) (dual of [35, 27, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
        the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3²²⁶, 2345, F₃, 45, 37) (dual of [(2345, 45), 105299, 38]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row