TY - JOUR
T1 - On the covering radius of Reed-Muller codes
AU - Cohen, Gérard D.
AU - Litsyn, Simon N.
PY - 1992/9/1
Y1 - 1992/9/1
N2 - We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the 'essence of Reed-Mullerity'. The idea is to find a 'seed' upper bound-a properly chosen combination of binomial coefficients-well fitted to the respective growths of m (log of length) and r (order), to initiate double induction on m and r. Suprisingly enough, these two simple ingredients suffice to essentially fill the gaps between lower and upper bounds, a result stated in our theorem.
AB - We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the 'essence of Reed-Mullerity'. The idea is to find a 'seed' upper bound-a properly chosen combination of binomial coefficients-well fitted to the respective growths of m (log of length) and r (order), to initiate double induction on m and r. Suprisingly enough, these two simple ingredients suffice to essentially fill the gaps between lower and upper bounds, a result stated in our theorem.
UR - https://www.scopus.com/pages/publications/38249008578
U2 - 10.1016/0012-365X(92)90542-N
DO - 10.1016/0012-365X(92)90542-N
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:38249008578
SN - 0012-365X
VL - 106-107
SP - 147
EP - 155
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - C
ER -