MinT - Information on Result #1060231

Information on Result #1060231

Linear OOA(3²⁰⁴, 2391496, F₃, 4, 16) (dual of [(2391496, 4), 9565780, 17]-NRT-code), using OOA 2-folding based on linear OOA(3²⁰⁴, 4782992, F₃, 2, 16) (dual of [(4782992, 2), 9565780, 17]-NRT-code), using

trace code [i] based on linear OOA(9¹⁰², 2391496, F₉, 2, 16) (dual of [(2391496, 2), 4782890, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9¹⁰², 4782992, F₉, 16) (dual of [4782992, 4782890, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹⁰², 4782993, F₉, 16) (dual of [4782993, 4782891, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
      1. linear OA(9⁹⁹, 4782969, F₉, 16) (dual of [4782969, 4782870, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(9³, 24, F₉, 2) (dual of [24, 21, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(9³, 80, F₉, 2) (dual of [80, 77, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 9²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]

Mode: Constructive and 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, 2391496, F₃, 4, 16) (dual of [(2391496, 4), 9565779, 17]-NRT-code)	[i]		OOA Duplication