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Maximum weight spectrum codes with reduced length (1806.05427v1)
Published 14 Jun 2018 in cs.IT and math.IT
Abstract: A q-ary linear code of dimension k is called a maximum weight spectrum (MWS) code if it has the maximum possible number (viz. (qk-1)/(q-1)) of different non-zero weights. We construct MWS codes from quasi-minimal codes, thus obtaining of much shorter length than hitherto known. By an averaging argument, we show the existence of MWS codes of even shorter length.