MinT - Information on Result #1084707

Information on Result #1084707

Linear OOA(3¹⁰⁰, 2391494, F₃, 4, 8) (dual of [(2391494, 4), 9565876, 9]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3², 4, F₃, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;14,3) [i]
linear OOA(3²⁷, 1195745, F₃, 4, 4) (dual of [(1195745, 4), 4782953, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁷, 1594321, F₃, 4, 4) (dual of [(1594321, 4), 6377257, 5]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3²⁷, 1594322, F₃, 2, 4) (dual of [(1594322, 2), 3188617, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (23, 27, 1594322)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁷¹, 1195745, F₃, 4, 8) (dual of [(1195745, 4), 4782909, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3⁷¹, 4782980, F₃, 8) (dual of [4782980, 4782909, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷¹, 4782983, F₃, 8) (dual of [4782983, 4782912, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(3⁷¹, 4782969, F₃, 8) (dual of [4782969, 4782898, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(3⁵⁷, 4782969, F₃, 7) (dual of [4782969, 4782912, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 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, 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(3¹⁰⁰, 2391493, F₃, 5, 8) (dual of [(2391493, 5), 11957365, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3¹⁰⁰, 2391493, F₃, 12, 8) (dual of [(2391493, 12), 28697816, 9]-NRT-code)	[i]		OOA Stacking with Additional Row