MinT - Information on Result #1164590

Information on Result #1164590

Linear OOA(2¹¹⁷, 87385, F₂, 8, 12) (dual of [(87385, 8), 698963, 13]-NRT-code), using OA 6-folding and stacking based on linear OA(2¹¹⁷, 524310, F₂, 12) (dual of [524310, 524193, 13]-code), using

2 times code embedding in larger space [i] based on linear OA(2¹¹⁵, 524308, F₂, 12) (dual of [524308, 524193, 13]-code), using
- 1 times truncation [i] based on linear OA(2¹¹⁶, 524309, F₂, 13) (dual of [524309, 524193, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(2¹¹⁵, 524288, F₂, 13) (dual of [524288, 524173, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
      - strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
        dual of repetition code with length 21 [i]
    4. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2¹¹⁹, 87385, F₂, 8, 12) (dual of [(87385, 8), 698961, 13]-NRT-code)	[i]		OOA Duplication