MinT - Information on Result #1528420

Information on Result #1528420

Linear OOA(3²⁰³, 4194350, F₃, 3, 18) (dual of [(4194350, 3), 12582847, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰³, 4194350, F₃, 2, 18) (dual of [(4194350, 2), 8388497, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²³, 49, F₃, 2, 9) (dual of [(49, 2), 75, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²³, 49, F₃, 9) (dual of [49, 26, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²³, 53, F₃, 9) (dual of [53, 30, 10]-code), using
      - 7 times truncation [i] based on linear OA(3³⁰, 60, F₃, 16) (dual of [60, 30, 17]-code), using
        strength reduction [i] based on linear OA(3³⁰, 60, F₃, 17) (dual of [60, 30, 18]-code), using
        extended quadratic residue code Q_e(60,3) [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(3²⁰³, 2097175, F₃, 5, 18) (dual of [(2097175, 5), 10485672, 19]-NRT-code)	[i]		OOA Folding