MinT - Information on Result #1604246

Information on Result #1604246

Linear OOA(3¹³⁴, 4194343, F₃, 4, 13) (dual of [(4194343, 4), 16777238, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁴, 4194343, F₃, 2, 13) (dual of [(4194343, 2), 8388552, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹³, 42, F₃, 2, 6) (dual of [(42, 2), 71, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (7, 13, 42)-net over F₃, using
    - linear code embedding found in a computer search [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(3¹³⁵, 4194343, F₃, 4, 13) (dual of [(4194343, 4), 16777237, 14]-NRT-code)	[i]		OOA Duplication