MinT - Information on Result #1532476

Information on Result #1532476

Linear OOA(3²⁴⁰, 4194396, F₃, 3, 21) (dual of [(4194396, 3), 12582948, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁰, 4194396, F₃, 2, 21) (dual of [(4194396, 2), 8388552, 22]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3³⁰, 95, F₃, 2, 10) (dual of [(95, 2), 160, 11]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³⁰, 95, F₃, 10) (dual of [95, 65, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(3³⁰, 121, F₃, 10) (dual of [121, 91, 11]-code), using
      - the BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â {1,17,33,…,24}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
2. linear OOA(3²¹⁰, 4194301, F₃, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²¹⁰, 8388602, F₃, 21) (dual of [8388602, 8388392, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(3²⁴⁰, 2097198, F₃, 5, 21) (dual of [(2097198, 5), 10485750, 22]-NRT-code)	[i]		OOA Folding