MinT - Information on Result #1522154

Information on Result #1522154

Linear OOA(3¹⁰⁷, 4194520, F₃, 3, 10) (dual of [(4194520, 3), 12583453, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰⁷, 4194520, F₃, 2, 10) (dual of [(4194520, 2), 8388933, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁶, 219, F₃, 2, 5) (dual of [(219, 2), 422, 6]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁶, 219, F₃, 5) (dual of [219, 203, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁶, 242, F₃, 5) (dual of [242, 226, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
2. linear OOA(3⁹¹, 4194301, F₃, 2, 10) (dual of [(4194301, 2), 8388511, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁹¹, 8388602, F₃, 10) (dual of [8388602, 8388511, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3¹⁰⁷, 2097260, F₃, 5, 10) (dual of [(2097260, 5), 10486193, 11]-NRT-code)	[i]		OOA Folding