MinT - Information on Result #904236

Information on Result #904236

Linear OOA(81¹⁶, 272365, F₈₁, 2, 5) (dual of [(272365, 2), 544714, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
- appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
  - Hamming code H(3,81) [i]
linear OOA(81¹³, 265722, F₈₁, 2, 5) (dual of [(265722, 2), 531431, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81¹³, 531444, F₈₁, 5) (dual of [531444, 531431, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(81¹³, 531441, F₈₁, 5) (dual of [531441, 531428, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(81¹⁰, 531441, F₈₁, 4) (dual of [531441, 531431, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81⁵³, 4466666, F₈₁, 2, 10) (dual of [(4466666, 2), 8933279, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁵⁷, 4466666, F₈₁, 2, 11) (dual of [(4466666, 2), 8933275, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs