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1. Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes

   https://doi.org/10.1007/s10623-020-00726-x  

   López, Hiram H. ; Matthews, Gretchen L. ; Soprunov, Ivan ( January 2020 , Designs, Codes and Cryptography)
2. Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels

   https://doi.org/10.1109/ITW.2018.8613428  

   Fazeli, Arman ; Hassani, Hamed ; Mondelli, Marco ; Vardy, Alexander ( November 2018 , Proceedings of the IEEE Information Theory Workshop (ITW))
3. Q-ary Asymmetric LOCO Codes: Constrained Codes Supporting Flash Evolution

   https://doi.org/10.1109/ISIT44484.2020.9174176  

   Hareedy, Ahmed ; Dabak, Beyza ; Calderbank, Robert ( June 2020 , IEEE International Symposium on Information Theory (ISIT 2020))

   Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and transmission. This paper introduces simple constrained codes that support non-binary physical gates in multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified if problematic patterns change with time. These codes are designed to mitigate inter-cell interference, which is a critical source of error in Flash devices. The new codes are called q-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes codes previously designed for single-level cell (SLC) Flash devices (ALOCO codes). QA-LOCO codes work for a Flash device with any number, q, of levels per cell. For q ≥ 4, we show that QA-LOCO codes can achieve rates greater than 0.95log 2 q information bits per coded symbol. Capacity-achieving rates, affordable encoding-decoding complexity, and ease of reconfigurability support the growing improvement of M/T/Q/P-LC Flash memory devices, as well as lifecycle management as the characteristics of these devices change with time. 

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4. Fiber bundle codes: breaking the n 1/2 polylog( n ) barrier for Quantum LDPC codes

   https://doi.org/10.1145/3406325.3451005  

   Hastings, Matthew B. ; Haah, Jeongwan ; O'Donnell, Ryan ( June 2021 , Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing)
5. Locally Repairable Convertible Codes: Erasure Codes for Efficient Repair and Conversion

   https://doi.org/10.1109/ISIT54713.2023.10206604  

   Maturana, Francisco ; Rashmi, K. V. ( June 2023 , IEEE)