Everything about Polynomial code

🧭 Start here: a 6-step reading path

1. Read the overview: Polynomial codeA 5-minute orientation
2. Skim a recent paper: Efficient BCH Code Encoding and Decoding Algorithm With Divisor-Distance-Based Polynomial Division for STT-MRAMInfluential work since 2022
3. Pick up a classic book: The applications of generalized Bezout's theorem to the codes from the curves in high dimensional spacesThe most-reprinted book on the subject
4. Read the landmark paper: Polynomial Codes Over Certain Finite FieldsCited 2,905 times
5. Go sideways: Mathematics of cyclic redundancy checksA closely related topic
6. Go sideways: BCH codeA closely related topic

🏆 Landmark papers (most cited)

• Polynomial Codes Over Certain Finite Fields

  I. S. Reed, G. Solomon · 1960 · Journal of the Society for Industrial and Applied Mathematics · 2,905 citations

• Polynomial Time Algorithms for Multicast Network Code Construction

  S. Jaggi, P. Sanders, P.A. Chou · 2005 · IEEE Transactions on Information Theory · 695 citations

• Polynomial weights and code constructions

  James L. Massey, Daniel J. Costello, Jorn Justesen · 1973 · IEEE Transactions on Information Theory · 159 citations

• On upper bounds for code distance and covering radius of designs in polynomial metric spaces

  G Fazekas, V.I Levenshtein · 1995 · Journal of Combinatorial Theory, Series A · 36 citations

• Unusual general error locator polynomial for the (23, 12, 7) golay code

  Chong-Dao Lee, Yaotsu Chang, Ho-Hsuan Chang · 2010 · IEEE Communications Letters · 13 citations

• A two-level QR code scheme based on polynomial secret sharing

  Sijia Liu, Zhengxin Fu, Bin Yu · 2019 · Multimedia Tools and Applications · 11 citations

• Generator Polynomial Model-Based Eye Diagram Estimation Method for Bose-Chaudhuri-Hocquenghem (BCH) Code and Reed-Solomon (RS) Code

  Junyong Park, Joungho Kim · 2020 · IEEE Transactions on Electromagnetic Compatibility · 11 citations

• Design of A Parallel Decoding Method for LDPC Code Generated via Primitive Polynomial

  Zhe Zhang, Liang Zhou, Zhi Heng Zhou · 2021 · Electronics · 8 citations

🆕 Influential since 2022

• Efficient BCH Code Encoding and Decoding Algorithm With Divisor-Distance-Based Polynomial Division for STT-MRAM

  Li Zhang, Yitao Ma, Tetsuo Endoh · 2023 · IEEE Transactions on Magnetics · 7 citations

• Polynomial interpolation cross-section parameterization method with the RMC Monte Carlo code

  Zhiyuan Feng, Conglong Jia, Shanfang Huang · 2022 · Annals of Nuclear Energy · 6 citations

• Polynomial-time plaintext recovery attacks on the IKKR code-based cryptosystems

  Terry Shue Chien Lau, Temasek Laboratories, National University of Singapore, 5A Engineering Drive 1, #09-02, Singapore 117411, Singapore, Chik How Tan · 2023 · Advances in Mathematics of Communications · 4 citations

• A numerical method for parallel calculation of the positional characteristic for error correction in a polyalphabetic polynomial modular code

  North Caucasus Federal University, I.A. Kalmykov, A.A. Olenev · 2025 · Computer Optics · 3 citations

• HSPA: High-Throughput Sparse Polynomial Multiplication for Code-based Post-Quantum Cryptography

  Pengzhou He, Yazheng Tu, Tianyou Bao · 2024 · ACM Transactions on Embedded Computing Systems · 2 citations

📚 Books worth reading

• 📕The applications of generalized Bezout's theorem to the codes from the curves in high dimensional spaces · 1996
• 📕Conversion from engineering units to telemetry counts on Dryden Flight simulatorsJay A. Fantini · 1998
• 📕Recent trends in ergodic theory and dynamical systemsSiddhartha Bhattacharya, Tarun Das · 2015
• 📕Topics in finite fieldsGermany) International Conference on Finite Fields and Applications (11th 2013 Magdeburg · 2015
• 📕Algebraic curves and cryptographyVijaya Kumar Murty · 2010
• An Introduction To Central Simple Algebras And Their Applications To Wireless CommunicationGregory Berhuy · 2013
• 📕Arithmetic, geometry, cryptography and coding theoryInternational Conference "Arithmetic, Geometry, Cryptography and Coding Theory" (13th 2011 Marseille, France) · 2012

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Mathematics of cyclic redundancy checks The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF(2) (the finite field of integers modulo…
• BCH code In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials…
• Linear code In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally…
• Cyclic code In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcti…
• Coding theory approaches to nucleic acid design DNA code construction refers to the application of coding theory to the design of nucleic acid systems for the field of DNA–based computation. DNA sequences…
• Binary Goppa code In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described…
• Folded Reed–Solomon code In coding theory, folded Reed–Solomon codes are like Reed–Solomon codes, which are obtained by mapping m {\displaystyle m} Reed–Solomon codewords over…
• Kraft–McMillan inequality In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version)…