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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…
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…
Explicit Subcodes of Reed-Solomon Codes that Efficiently Achieve List Decoding Capacity
Amit Berman, Yaron Shany, Itzhak Tamo
In this paper, we introduce a novel explicit family of subcodes of Reed-Solomon (RS) codes that efficiently achieve list decoding capacity with a constant output list size. Our app…
Fast syndrome-based Chase decoding of binary BCH codes through Wu list decoding
Yaron Shany, Amit Berman
We present a new fast Chase decoding algorithm for binary BCH codes. The new algorithm reduces the complexity in comparison to a recent fast Chase decoding algorithm for Reed--Solo…
Repairing Reed-Solomon Codes Evaluated on Subspaces
Amit Berman, Sarit Buzaglo, Avner Dor +2
We consider the repair problem for Reed--Solomon (RS) codes, evaluated on an -linear subspace of dimension , where is a prime powe…