6 papers
Entanglement-assisted quantum locally recoverable codes: bounds and constructions with availability
Gretchen L. Matthews, Rutuja Kshirsagar, Julia Shapiro
In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to erased qudits can be recovered from any one of $t…
List-Decodable Folded Quantum Hermitian Codes
Gretchen L. Matthews, Julia Shapiro
Folded Reed-Solomon codes, introduced by Guruswami and Rudra in 2007, have been shown to achieve the information-theoretically best possible trade-off between the rate of a code an…
Combinatorial Analysis of Dyadic and Quasi-Dyadic Codes
Anthony Gómez-Fonseca, Gretchen L. Matthews, Kirsten D. Morris +1
Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly in…
Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves
Monica Lichtenwalner, Hiram H. López, Gretchen L. Matthews +1
Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphis…
Pseudocodewords of quantum, quasi-cyclic, and spatially-coupled LDPC codes: a fundamental cone perspective
Wittawat Kositwattanarerk, Gretchen L. Matthews, Emily McMillon +1
While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudo…
A Combinatorial Approach to Avoiding Weak Keys in the BIKE Cryptosystem
Gretchen L Matthews, Emily McMillon
Bit Flipping Key Encapsulation (BIKE) is a code-based cryptosystem that was considered in Round 4 of the NIST Post-Quantum Cryptography Standardization process. It is based on quas…