A search technique for quasi-perfect codes
نویسندگان
چکیده
منابع مشابه
Hypothesis Testing and Quasi-Perfect Codes
Hypothesis testing lower bounds to the channel coding error probability are studied. For a family of symmetric channels, block lengths and coding rates, the error probability of the best code is shown to coincide with that of a binary hypothesis test with certain parameters. The points in which they coincide, are precisely the points at which perfect or quasi-perfect codes exist. General condit...
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We consider quasi-perfect codes in Z over the `p metric, 2 ≤ p <∞. Through a computational approach, we determine all radii for which there are linear quasi-perfect codes for p = 2 and n = 2, 3. Moreover, we study codes with a certain degree of imperfection, a notion that generalizes the quasi-perfect codes. Numerical results concerning the codes with the smallest degree of imperfection are pre...
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A mapping f from F2m to itself is almost perfect nonlinear (APN) if its directional derivatives in nonzero directions are all 2-to-1. Let Cf be the binary linear code of length 2 − 1, whose parity check matrix has its j-th column [ π f(π) ] , where π is a primitive element in F2m and j = 0, 1, · · · , 2 − 2. For m ≥ 3 and any quadratic APN function f(x) = ∑m−1 i,j=0 ai,jx 2+2 , ai,j ∈ F2m , it ...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1966
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(66)90128-8