MinT - Information on Result #1528612

Information on Result #1528612

Linear OOA(3²⁰⁵, 4194369, F₃, 3, 18) (dual of [(4194369, 3), 12582902, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰⁵, 4194369, F₃, 2, 18) (dual of [(4194369, 2), 8388533, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁵, 68, F₃, 2, 9) (dual of [(68, 2), 111, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁵, 68, F₃, 9) (dual of [68, 43, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁵, 80, F₃, 9) (dual of [80, 55, 10]-code), using
      - the primitive cyclic code C(A) with length 80Â = 3⁴âˆ’1, defining set AÂ =Â {0,1,2,4,5,7,53}, and minimum distance dÂ â‰¥ |{−1,0,…,7}|+1Â =Â 10 (BCH-bound) [i]
2. linear OOA(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(3²⁰⁵, 2097184, F₃, 5, 18) (dual of [(2097184, 5), 10485715, 19]-NRT-code)	[i]		OOA Folding