Doubly and triply extended MSRD codes
Umberto Mart\'inez-Pe\~nas
TL;DR
This paper generalizes doubly and triply extended Reed--Solomon codes, characterizes when multiply extended codes reach the Singleton bound, and introduces new families of MSRD codes with specific properties.
Contribution
It provides a general characterization for when multiply extended codes attain the Singleton bound and constructs new families of MSRD codes including known special cases.
Findings
Several new families of MSRD codes are constructed.
Conditions for codes to be one-weight are discussed.
General criteria for codes to attain the Singleton bound are established.
Abstract
In this work, doubly extended linearized Reed--Solomon codes and triply extended Reed--Solomon codes are generalized. We obtain a general result in which we characterize when a multiply extended code for a general metric attains the Singleton bound. We then use this result to obtain several families of doubly extended and triply extended maximum sum-rank distance (MSRD) codes that include doubly extended linearized Reed--Solomon codes and triply extended Reed--Solomon codes as particular cases. To conclude, we discuss when these codes are one-weight codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding