Abstract
It is proved that the covering radius of a primitive binary BCH code of length q-1 and designed distance 2t+1, where EquationSource % MathType!MTEF!2!1!+- feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyCaiabg2 % da9iaaikdadaahaaWcbeqaaiaad2gaaaGccqGH+aGpdaWadaqaamaa % bmaabaGaaGOmaiaadshacqGHsislcaaIZaaacaGLOaGaayzkaaWaae % WaaeaacaaIYaGaamiDaiabgkHiTiaaigdaaiaawIcacaGLPaaacaGG % HaaacaGLBbGaayzxaaWaaWbaaSqabeaacaaIYaaaaOGaaiilaaaa!48DE! is exactly 2t-1 (the minimum value possible). The bound for q is significantly lower than the one obtained by O. Moreno and C. J. Moreno [9].
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Cohen, S.D. The Length of Primitive BCH Codes with Minimal Covering Radius. Designs, Codes and Cryptography 10, 5–16 (1997). https://doi.org/10.1023/A:1008299101833
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DOI: https://doi.org/10.1023/A:1008299101833