MinT - Information on Result #1523709

Information on Result #1523709

Linear OOA(3¹³⁹, 4194411, F₃, 3, 13) (dual of [(4194411, 3), 12583094, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁹, 4194411, F₃, 2, 13) (dual of [(4194411, 2), 8388683, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁸, 110, F₃, 2, 6) (dual of [(110, 2), 202, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁸, 110, F₃, 6) (dual of [110, 92, 7]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. linear OA(3¹⁷, 108, F₃, 6) (dual of [108, 91, 7]-code), using
        codes constructed by inverting constructionÂ Y₁ [i]
      2. linear OA(3¹⁷, 109, F₃, 5) (dual of [109, 92, 6]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 87 402097 [i]
      3. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 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]
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(3¹³⁹, 2097205, F₃, 5, 13) (dual of [(2097205, 5), 10485886, 14]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹³⁹, 2097205, F₃, 15, 13) (dual of [(2097205, 15), 31457936, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row