MinT - Information on Result #1010630

Information on Result #1010630

Linear OOA(3¹⁵⁹, 3188703, F₃, 3, 12) (dual of [(3188703, 3), 9565950, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁷, 53, F₃, 3, 6) (dual of [(53, 3), 142, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. linear OOA(3¹², 33, F₃, 3, 6) (dual of [(33, 3), 87, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 12, 33)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁴², 3188650, F₃, 3, 12) (dual of [(3188650, 3), 9565808, 13]-NRT-code), using
- trace code [i] based on linear OOA(9⁷¹, 1594325, F₉, 3, 12) (dual of [(1594325, 3), 4782904, 13]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(9⁷¹, 4782975, F₉, 12) (dual of [4782975, 4782904, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁷¹, 4782976, F₉, 12) (dual of [4782976, 4782905, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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(3¹⁵⁹, 1594351, F₃, 15, 12) (dual of [(1594351, 15), 23915106, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row