MinT - Information on Result #1119318

Information on Result #1119318

Linear OOA(3²³⁹, 5033262, F₃, 5, 14) (dual of [(5033262, 5), 25166071, 15]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3²⁸, 1677754, F₃, 5, 4) (dual of [(1677754, 5), 8388742, 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, 1677754, F₃, 5, 7) (dual of [(1677754, 5), 8388709, 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(3¹⁵⁰, 1677754, F₃, 5, 14) (dual of [(1677754, 5), 8388620, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁴, 34, F₃, 5, 7) (dual of [(34, 5), 156, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
      - linear code embedding found in a computer search [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(3²⁴⁰, 5033262, F₃, 5, 14) (dual of [(5033262, 5), 25166070, 15]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²⁴¹, 5033262, F₃, 5, 14) (dual of [(5033262, 5), 25166069, 15]-NRT-code)	[i]		OOA Duplication