MinT - Information on Result #1645124

Information on Result #1645124

Linear OOA(3¹⁵⁸, 142421, F₃, 5, 20) (dual of [(142421, 5), 711947, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁸, 142421, F₃, 3, 20) (dual of [(142421, 3), 427105, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵⁸, 177151, F₃, 3, 20) (dual of [(177151, 3), 531295, 21]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁵⁷, 177151, F₃, 3, 20) (dual of [(177151, 3), 531296, 21]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁵⁷, 531453, F₃, 20) (dual of [531453, 531296, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(3¹⁵⁷, 531441, F₃, 20) (dual of [531441, 531284, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(3¹⁴⁵, 531441, F₃, 19) (dual of [531441, 531296, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(3⁰, 12, F₃, 0) (dual of [12, 12, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3¹⁵⁸, 71210, F₃, 25, 20) (dual of [(71210, 25), 1780092, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row