This paper presents a family of high-rate Low-Density Parity-Check (LDPC) quantum error correction (QEC) codes, known as *La-cross codes*, designed for neutral atom qubit registers. These codes are analyzed for their performance in quantum error correction and compared to surface codes. The La-cross codes are constructed using hypergraph product (HGP) methods, with stabilizers that include long-range interactions, which enhance their error suppression capabilities. Through circuit-level simulations, the authors find that these codes outperform surface codes in terms of logical error probability when the two-qubit nearest neighbour gate error probability is below 0.1%. The codes can be integrated into two-dimensional static neutral atom qubit architectures with open boundaries, where long-range connectivity is achieved through Rydberg-blockade interactions. The paper also discusses the implementation details, including the use of multiple laser colors to enable transitions to different Rydberg states for different interatomic distances, and the impact of gate errors on the logical error probability. The results show that La-cross codes offer significant advantages in terms of qubit overhead and error suppression, making them promising candidates for near-term quantum computing platforms.This paper presents a family of high-rate Low-Density Parity-Check (LDPC) quantum error correction (QEC) codes, known as *La-cross codes*, designed for neutral atom qubit registers. These codes are analyzed for their performance in quantum error correction and compared to surface codes. The La-cross codes are constructed using hypergraph product (HGP) methods, with stabilizers that include long-range interactions, which enhance their error suppression capabilities. Through circuit-level simulations, the authors find that these codes outperform surface codes in terms of logical error probability when the two-qubit nearest neighbour gate error probability is below 0.1%. The codes can be integrated into two-dimensional static neutral atom qubit architectures with open boundaries, where long-range connectivity is achieved through Rydberg-blockade interactions. The paper also discusses the implementation details, including the use of multiple laser colors to enable transitions to different Rydberg states for different interatomic distances, and the impact of gate errors on the logical error probability. The results show that La-cross codes offer significant advantages in terms of qubit overhead and error suppression, making them promising candidates for near-term quantum computing platforms.