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cs.IT2026
Codes with Large Minimum Distance in Product Codes: Explicit Constructions and Bounds
Amit Berman, Yaron Shany, Itzhak Tamo
Products of MDS codes are of major practical importance; for a recent example, they are used in Data Availability Sampling (DAS) in blockchain networks such as Celestia and as part…
cs.IT2024
The Generating Idempotent Is a Minimum-Weight Codeword for Some Binary BCH Codes
Yaron Shany, Amit Berman
In a paper from 2015, Ding et al. (IEEE Trans. IT, May 2015) conjectured that for odd , the minimum distance of the binary BCH code of length and designed distance $2^{m…
cs.IT2024
Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes
Amit Berman, Yaron Shany, Itzhak Tamo
We present algorithms for specifying the support of minimum-weight words of extended binary BCH codes of length and designed distance $d(m,s,i):=2^{m-1-s}-2^{m-1-i…