MinT - Information on Result #1060237

Information on Result #1060237

Linear OOA(3²¹⁸, 2495735, F₃, 4, 16) (dual of [(2495735, 4), 9982722, 17]-NRT-code), using OOA 2-folding based on linear OOA(3²¹⁸, 4991470, F₃, 2, 16) (dual of [(4991470, 2), 9982722, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁶⁷, 797169, F₃, 2, 8) (dual of [(797169, 2), 1594271, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁶⁷, 1594338, F₃, 8) (dual of [1594338, 1594271, 9]-code), using
    - constructionÂ X4 applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(3⁶⁶, 1594323, F₃, 8) (dual of [1594323, 1594257, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(3⁵³, 1594323, F₃, 7) (dual of [1594323, 1594270, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3¹⁴, 15, F₃, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
        dual of repetition code with length 15 [i]
      4. linear OA(3¹, 15, F₃, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OOA(3¹⁵¹, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁹, 2495735, F₃, 4, 16) (dual of [(2495735, 4), 9982721, 17]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²²⁰, 2495735, F₃, 4, 16) (dual of [(2495735, 4), 9982720, 17]-NRT-code)	[i]		OOA Duplication