MinT - Information on Result #2478616

Information on Result #2478616

Linear OOA(2¹⁵⁷, 262156, F₂, 2, 17) (dual of [(262156, 2), 524155, 18]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁵⁵, 262155, F₂, 2, 17) (dual of [(262155, 2), 524155, 18]-NRT-code), using

OOA 2-folding [i] based on linear OA(2¹⁵⁵, 524310, F₂, 17) (dual of [524310, 524155, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2¹⁵⁴, 524309, F₂, 17) (dual of [524309, 524155, 18]-code), using
  - constructionÂ X4 applied to C_e(16) âŠ‚ C_e(14) [i] based on
    1. linear OA(2¹⁵³, 524288, F₂, 17) (dual of [524288, 524135, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(2¹³⁴, 524288, F₂, 15) (dual of [524288, 524154, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2¹⁵⁸, 262156, F₂, 2, 17) (dual of [(262156, 2), 524154, 18]-NRT-code)	[i]		OOA Duplication