MinT - Information on Result #900390

Information on Result #900390

Linear OOA(27¹⁶, 10600, F₂₇, 2, 5) (dual of [(10600, 2), 21184, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27³, 757, F₂₇, 2, 2) (dual of [(757, 2), 1511, 3]-NRT-code), using
- appending kth column [i] based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
  - Hamming code H(3,27) [i]
linear OOA(27¹³, 9843, F₂₇, 2, 5) (dual of [(9843, 2), 19673, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27¹³, 19686, F₂₇, 5) (dual of [19686, 19673, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(27¹³, 19683, F₂₇, 5) (dual of [19683, 19670, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(27¹⁰, 19683, F₂₇, 4) (dual of [19683, 19673, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(27⁶², 4204901, F₂₇, 2, 10) (dual of [(4204901, 2), 8409740, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(27⁶⁷, 4204901, F₂₇, 2, 11) (dual of [(4204901, 2), 8409735, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs