MinT - Information on Result #1008879

Information on Result #1008879

Linear OOA(7⁹², 3843206, F₇, 3, 12) (dual of [(3843206, 3), 11529526, 13]-NRT-code), using trace code based on linear OOA(49⁴⁶, 1921603, F₄₉, 3, 12) (dual of [(1921603, 3), 5764763, 13]-NRT-code), using

OOA 3-folding [i] based on linear OA(49⁴⁶, 5764809, F₄₉, 12) (dual of [5764809, 5764763, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁴⁶, 5764810, F₄₉, 12) (dual of [5764810, 5764764, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(9) [i] based on
    1. linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(49³⁷, 5764801, F₄₉, 10) (dual of [5764801, 5764764, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(49¹, 9, F₄₉, 1) (dual of [9, 8, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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		Method
1	Linear OOA(7⁹³, 3843206, F₇, 3, 12) (dual of [(3843206, 3), 11529525, 13]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(7⁹⁹, 3843219, F₇, 3, 12) (dual of [(3843219, 3), 11529558, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(7¹⁰⁴, 3843306, F₇, 3, 12) (dual of [(3843306, 3), 11529814, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs