MinT - Information on Result #1013983

Information on Result #1013983

Linear OOA(7⁸⁸, 39231, F₇, 3, 16) (dual of [(39231, 3), 117605, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁹, 13, F₇, 3, 8) (dual of [(13, 3), 30, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 9, 13)-net over F₇, using
  - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁷⁹, 39218, F₇, 3, 16) (dual of [(39218, 3), 117575, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁷⁹, 117654, F₇, 16) (dual of [117654, 117575, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁷⁹, 117655, F₇, 16) (dual of [117655, 117576, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
      1. linear OA(7⁷⁹, 117649, F₇, 16) (dual of [117649, 117570, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 7⁶âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(7⁷³, 117649, F₇, 15) (dual of [117649, 117576, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 7⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(7⁰, 6, F₇, 0) (dual of [6, 6, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(7⁸⁹, 39231, F₇, 3, 16) (dual of [(39231, 3), 117604, 17]-NRT-code)	[i]		OOA Duplication