MinT - Information on Result #1117170

Information on Result #1117170

Linear OOA(3⁷⁷, 11818, F₃, 5, 11) (dual of [(11818, 5), 59013, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶, 7, F₃, 5, 5) (dual of [(7, 5), 29, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁷¹, 11811, F₃, 5, 11) (dual of [(11811, 5), 58984, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3⁷¹, 59055, F₃, 11) (dual of [59055, 58984, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷¹, 59059, F₃, 11) (dual of [59059, 58988, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(3⁷¹, 59049, F₃, 11) (dual of [59049, 58978, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(3⁶¹, 59049, F₃, 10) (dual of [59049, 58988, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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(3⁷⁷, 11817, F₃, 15, 11) (dual of [(11817, 15), 177178, 12]-NRT-code)	[i]		OOA Stacking with Additional Row