Strong blocking sets and minimal codes from expander graphs
From MaRDI portal
Publication:6571606
DOI10.1090/tran/9205zbMATH Open1543.51007MaRDI QIDQ6571606
Shagnik Das, Alessandro Neri, Anurag Bishnoi, Noga Alon
Publication date: 12 July 2024
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Linear codes and caps in Galois spaces (51E22) Combinatorial aspects of finite geometries (05B25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Blocking sets, ovals, (k)-arcs (51E21) Connectivity (05C40) Expander graphs (05C48)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Yet another variation on minimal linear codes
- Lines in higgledy-piggledy arrangement
- Search problems in vector spaces
- Linear nonbinary covering codes and saturating sets in projective spaces
- Linear binary codes with intersection properties
- Linear intersecting codes
- Ramanujan graphs
- On the second eigenvalue of a graph
- A survey of integrity
- Covering finite fields with cosets of subspaces
- The blocking number of an affine space
- Existence and explicit constructions of \(q+1\) regular Ramanujan graphs for every prime power \(q\)
- On the asymptotic behaviour of some towers of function fields over finite fields
- Two results about the hypercube
- The integrity of a cubic graph
- A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
- Minimal linear codes arising from blocking sets
- A geometric characterization of minimal codes and their asymptotic performance
- On cutting blocking sets and their codes
- Explicit expanders of every degree and size
- Pseudorandomness
- Linear Codes From Some 2-Designs
- Expander codes
- Field reduction and linear sets in finite geometry
- Expander graphs and their applications
- Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
- Decoding linear block codes for minimizing word error rate (Corresp.)
- A recursive approach to low complexity codes
- Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
- Minimal vectors in linear codes
- Intersecting codes and independent families
- Explicit, almost optimal, epsilon-balanced codes
- Full Characterization of Minimal Linear Codes as Cutting Blocking Sets
- Algebraic geometry codes and some applications
- Short Minimal Codes and Covering Codes via Strong Blocking Sets in Projective Spaces
- Three Combinatorial Perspectives on Minimal Codes
- Asymptotic Bounds on the Integrity of Graphs and Separator Theorems for Graphs
- Minimal Linear Codes in Odd Characteristic
- Class of constructive asymptotically good algebraic codes
- On a problem of K. Zarankiewicz
- Small Strong Blocking Sets by Concatenation
- Explicit constructions of perfect hash families from algebraic curves over finite fields
- On the lower bound for the length of minimal codes
- Outer strong blocking sets
Related Items (1)
This page was built for publication: Strong blocking sets and minimal codes from expander graphs