1
Introduction and Setup
2
Preliminaries
▶
2.1
Codes and basic parameters
2.2
The field trace and inner products
2.3
The Gilbert–Varshamov bound and the goal
2.4
Concatenated codes and default parameters
2.5
Weight distribution of the inner code
2.6
Fourier analysis over \(\mathbb {F}_2^{k_0 n}\)
2.7
Standard probabilistic and combinatorial facts
3
A Useful Moment Computation
4
Most Linear Codes \(\mathcal{C}_{\mathrm{out}}\) Work Well
5
A Soft-Decoding Sufficient Condition
6
A High Min-Entropy Sufficient Condition
Dependency graph
When Do Low-Rate Concatenated Codes Approach the Gilbert–Varshamov Bound?
Doron, Mosheiff, Wootters (blueprint)
1
Introduction and Setup
2
Preliminaries
2.1
Codes and basic parameters
2.2
The field trace and inner products
2.3
The Gilbert–Varshamov bound and the goal
2.4
Concatenated codes and default parameters
2.5
Weight distribution of the inner code
2.6
Fourier analysis over \(\mathbb {F}_2^{k_0 n}\)
2.7
Standard probabilistic and combinatorial facts
3
A Useful Moment Computation
4
Most Linear Codes \(\mathcal{C}_{\mathrm{out}}\) Work Well
5
A Soft-Decoding Sufficient Condition
6
A High Min-Entropy Sufficient Condition