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Trace codes over Z 4 , and Boolean functions

Abstract : We construct trace codes over Z 4 based on Boolean functions and their support. The Lee weight distribution of these codes is studied by using the Walsh-Hadamard transform of the Boolean functions, and exponential character sums. We obtain few weights codes. In particular, bent and semi-bent functions give three-weight codes.
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https://hal.archives-ouvertes.fr/hal-02411617
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Submitted on : Tuesday, December 17, 2019 - 10:44:44 AM
Last modification on : Saturday, June 25, 2022 - 9:13:36 PM
Long-term archiving on: : Wednesday, March 18, 2020 - 1:01:51 PM

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Minjia Shi, Yan Liu, Hugues Randriambololona, Lin Sok, Patrick Sole. Trace codes over Z 4 , and Boolean functions. Designs, Codes and Cryptography, Springer Verlag, 2019, 87, pp.1447 - 1455. ⟨10.1007/s10623-018-0542-x⟩. ⟨hal-02411617⟩

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