MinT - Information on Result #2422041

Information on Result #2422041

Linear OOA(2¹⁷⁰, 112, F₂, 2, 66) (dual of [(112, 2), 54, 67]-NRT-code), using strength reduction based on linear OOA(2¹⁷⁰, 112, F₂, 2, 67) (dual of [(112, 2), 54, 68]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8³⁸, 28, F₈, 2, 33) (dual of [(28, 2), 18, 34]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,22P) [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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		Method
1	Linear OOA(2¹⁷², 113, F₂, 2, 66) (dual of [(113, 2), 54, 67]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁷⁴, 114, F₂, 2, 66) (dual of [(114, 2), 54, 67]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁶, 115, F₂, 2, 66) (dual of [(115, 2), 54, 67]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁸, 116, F₂, 2, 66) (dual of [(116, 2), 54, 67]-NRT-code)	[i]
5	Linear OOA(2¹⁷¹, 112, F₂, 2, 66) (dual of [(112, 2), 53, 67]-NRT-code)	[i]	OOA Duplication
6	Linear OOA(2¹⁷⁰, 56, F₂, 4, 66) (dual of [(56, 4), 54, 67]-NRT-code)	[i]	OOA Folding