MinT - Information on Result #1523820

Information on Result #1523820

Linear OOA(3¹⁴¹, 4194502, F₃, 3, 13) (dual of [(4194502, 3), 12583365, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴¹, 4194502, F₃, 2, 13) (dual of [(4194502, 2), 8388863, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁰, 201, F₃, 2, 6) (dual of [(201, 2), 382, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰, 201, F₃, 6) (dual of [201, 181, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁰, 242, F₃, 6) (dual of [242, 222, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. linear OOA(3¹²¹, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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(3¹⁴¹, 2097251, F₃, 5, 13) (dual of [(2097251, 5), 10486114, 14]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁴¹, 2097250, F₃, 15, 13) (dual of [(2097250, 15), 31458609, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row