MinT - Information on Result #1008699

Information on Result #1008699

Linear OOA(3¹⁴⁸, 3188658, F₃, 3, 12) (dual of [(3188658, 3), 9565826, 13]-NRT-code), using trace code based on linear OOA(9⁷⁴, 1594329, F₉, 3, 12) (dual of [(1594329, 3), 4782913, 13]-NRT-code), using

OOA 3-folding [i] based on linear OA(9⁷⁴, 4782987, F₉, 12) (dual of [4782987, 4782913, 13]-code), using
- 2 times code embedding in larger space [i] based on linear OA(9⁷², 4782985, F₉, 12) (dual of [4782985, 4782913, 13]-code), using
  - constructionÂ X4 applied to C_e(11) âŠ‚ C_e(9) [i] based on
    1. 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]
    2. linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(9¹⁵, 16, F₉, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,9)), using
      - dual of repetition code with length 16 [i]
    4. linear OA(9¹, 16, F₉, 1) (dual of [16, 15, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(9¹, 728, F₉, 1) (dual of [728, 727, 2]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 9³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [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(3¹⁴⁹, 3188658, F₃, 3, 12) (dual of [(3188658, 3), 9565825, 13]-NRT-code)	[i]		OOA Duplication