MinT - Information on Result #1081260

Information on Result #1081260

Linear OOA(3²⁴², 4194318, F₃, 4, 16) (dual of [(4194318, 4), 16777030, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷⁸, 2097151, F₃, 4, 8) (dual of [(2097151, 4), 8388526, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3⁷⁸, 4194302, F₃, 2, 8) (dual of [(4194302, 2), 8388526, 9]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(3⁷⁶, 4194301, F₃, 2, 8) (dual of [(4194301, 2), 8388526, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3⁷⁶, 8388602, F₃, 8) (dual of [8388602, 8388526, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁶⁴, 2097167, F₃, 4, 16) (dual of [(2097167, 4), 8388504, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹³, 17, F₃, 4, 8) (dual of [(17, 4), 55, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (5, 13, 17)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁵¹, 2097150, F₃, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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

None.