MinT - Information on Result #1119323

Information on Result #1119323

Linear OOA(3²⁴⁶, 5033412, F₃, 5, 14) (dual of [(5033412, 5), 25166814, 15]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3²⁸, 1677804, F₃, 5, 4) (dual of [(1677804, 5), 8388992, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁸, 2391484, F₃, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3²⁸, 2391485, F₃, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁶¹, 1677804, F₃, 5, 7) (dual of [(1677804, 5), 8388959, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁶¹, 2796200, F₃, 5, 7) (dual of [(2796200, 5), 13980939, 8]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OA(3⁶¹, 8388601, F₃, 7) (dual of [8388601, 8388540, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(3¹⁵⁷, 1677804, F₃, 5, 14) (dual of [(1677804, 5), 8388863, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²¹, 84, F₃, 5, 7) (dual of [(84, 5), 399, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (14, 21, 84)-net over F₃, using
      - trace code for nets [i] based on digital (0, 7, 28)-net over F₂₇, using
        net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
        the rational function field F₂₇(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(3¹³⁶, 1677720, F₃, 5, 14) (dual of [(1677720, 5), 8388464, 15]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(3¹³⁶, 8388600, F₃, 14) (dual of [8388600, 8388464, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(3²⁴⁷, 5033412, F₃, 5, 14) (dual of [(5033412, 5), 25166813, 15]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²⁴⁸, 5033412, F₃, 5, 14) (dual of [(5033412, 5), 25166812, 15]-NRT-code)	[i]		OOA Duplication